RJR, can you confirm your 470uF is indeed BEFORE the LM317T per GRJ's schematic?
If it's practical to temporarily disconnnect the current-hungry incandescent markers from your circuit I think it wise to confirm the 470uF is doing its job.
Would you consider using LEDs for your markers for the Williams? In general LEDs should get you a 5x-10x current reduction vs. traditional incandescents.
I don't mess around using analog regulators as Buck Converters are much more efficient.
Infact been kicking around the idea of mounting the Buck in a baggage car and then tying all the cars together with mini 2 pin plugs. Also in the baggage car will be a LiOn battery powering all the lights. Then can remove all the power pickup rollers to get rid of the drag. We do this in the large scale world and it works great along with using ball bearings in the journal boxes.
Do you operate TMCC by any chance? I was messing with these <$2 converters a while back and noticed the 3rd harmonic of the LM2596 switching frequency is smack dab in the middle of TMCC carrier. I don't use TMCC but was wondering if you (or anyone) have had any interference problems.
I think your idea of daisy-chaining power is fantastic - not just to remove mechanical drag but all that roller noise!
Stan: It is across the output of the bridge rectifier, which makes it before theregulator. The first car I converted did not have marker lights. I am not getting flicker. I'm getting ground that cuts off due to poor design by Williams. Wheel to frame contact is poor and intermittent. Lamps go out rather than flicker.
RJR: what's your track voltage? And can you measure the voltage across the 470uF (or between + and - of bridge)?
By all means improve the mechanical ground axle connections if you can, but I'm baffled why you aren't seeing some improvement from the 470uF...unless it is not getting enough voltage in the first place...
The incandescent bulbs are a problem, I'd run those directly from track voltage, perhaps in series since they're probably 12V bulbs.
OK, here's some results:
I was right about the ground. The 2nd car I converted, a Williams madison-style observation care, is the one with 2 grain-of-wheat bulbs. I would not call them power hungry, and they work fine tied into the 10.1 volt regulated power supply they share with two strips of led lights. (This is one benefit of setting up the regulators to provide constant voltage rather than constant current---I can turn out a bunch of them and use them interchangeably for various lighting loads. I removed the trucks. They & the frame are heavily painted. I used a moto-tool with drum sander to remove all the paint from the area where they mount--top of the trucks and bottom & top of the frame by the hole. Vast improvement, for now there are more paths for ground. Now the lights only flash off---not flicker--- where the center rail has dirt; when I wipe the center rail with Brakleen, a lot of dirt comes off and the lights don't cut off.
The adjoining car, which is the first I converted, has the lights go out often, especially on curves. I intend to remove the trucks and do the same. Both cars have 470mfd capacitors.
I intend to do the remaining pair of Williams Madison cars and a 5-car Williams streamliner, and then turn to the cabeese. I do not intend to tackle my 9-car MTH passenger set, since the stock lighting is even and flicker-free.
Stan: My track voltage is about 18VAC. I haven't measured the voltage with the car on the track, but I can tell you that on my workbench, applying 10 VAC to the rectifier input, with a 1000mfd cap, will yield about 13 VDC.
Given that I'm using 2 LED strips in a car, it may well be that a 470mfd cap can't provide power for a long enough period. As I said, the lights do out when there is a very brief power outage. There is no flicker (which I define as a constantly changing brightness) in the converted cars, which is quite evident in the unconverted incandescent cars. It is possible, of course, to put a very large capacitor in the rectifier output to provide power for a longer period. But I'd rather address the crux of the issue, the poor ground, rather than just mask it with a larger cap.
It would probably be best to drill and tap each truck for a very small screw, to hold a #24 wire connected to the frame. 24 gauge should carry enough current for the LED lighting.
At 10V, 2 LED strips plus the LM317 draws about 25 mA. The voltage on the cap droops at I/C or 25 mA / 470 uF = 50 Volts/sec. Your track voltage is 18VAC so your cap starts at, say, 23V. At your relatively small load current, the LM317 needs about 1.5V of input headroom above its 10V regulated output. So a 470uF cap can power the LEDs for about 1/4 sec.
Stan, I'll accept your calcs as correct. When the lights go out, they are off for more than 1/4 second. I'll assume, per your calcs, that it is 1/4 sec before they go off.
I cut a bunch of pegboard and am assembling 9 units on an assembly line basis. I made one with a 1000mfd capacitor, and before completing the rest will see if that makes a difference. A 1000mfd cap has to be lying on its side, unless I want to add on to one of its leads. I may just go back to 470's.
You can address the flicker in a couple of ways. Obviously, the easy way is to increase the size of the capacitor.
I'm a bit surprised you have all those grounding issues, I've converted a set of K-Line passenger cars, and a set of MTH Premier cars, and I happened to use the 470uf cap with a bridge rectifier and the LM317 in constant current mode. I've run them on the club layout and here, and the lighting is steady as a rock.
With the size of your power module, I can't see why you can't use a 2200uf 35v cap laying on it's side and keep the same profile, that would greatly increase the flicker resistance. While it's certainly good to reduce the ground issues, that seems to be a lot more work. 
Another thought is that the 10V value leaves little headroom, those LED's will be dark at 9 volts or so. However, the constant current circuit degrades gracefully and will reduce the effects of the poor contact.
I note you did not mention Williams cars. There's the difference.
I've also done Williams cars, I had a set of the 15" aluminum ones, and I put LED's in those. I had zero flicker.
This is not rocket science, it's quite possible to get perfect lighting with just component selection, and it's far easier than taking apart trucks and doing mods, etc.
Not when the lights can stay off for several seconds. These are plastic cars.
How much is it worth to you to get a circuit that will light them for as long as you like? 
$0.00
Hmm... I guess that's out. 
I finally got disgusted with the grounding issue on the Williams Madison cars, and decided to tap the truck frame to fasten a grounding wire to do it. Attached are 3 pictures of the process. The first shows the raw truck. Note the hole, tapped for a screw that comes through the car frame. The area around it was covered with heavy black paint, which I had sanded off with a moto-tool to try to improve the contact.
The 2nd picture shows where, using a #43 drill, I drilled the truck frame vertically between the mounting screw and the coupler, then tapping the hole wiht a 4-40 tap.
The 3rd picture shows a bare crimp connector attached, with the wire going through the frame in the large hole that was there for the hot wire.
Performance is much improved.
GRJ: I also converted the lights in a Williams streamliner. That truck is much different, having a stud on the truck, held by a horseshoe clip inside the car. That's probably the type you encountered.
OH, if the truck was depending on the attachment point to conduct ground, it's no surprise that you had grounding issues! Yes, mine have all had a ground wire coming up from the truck.
For other power installation, like the ERR TMCC controlled Milk Car, I actually run a ground wire from the truck to insure a good ground.
Attached is a photo of my final configuration for the voltage regulator circuit, using a 470uf capacitor and outputting 10.1 VDC. Size is 2" long by 1/2" wide by 1" high. Wires have been led out through top of board to permit installation to car floor using thick, soft double-sided tape.
I turned out 10 identical units on an assembly line basis for installation in cars and buildings.
Too late for those, but I'd recommend laying the components down on the board. The size of the board is sufficient for them all to still fit, and you get a much lower profile board.
This was intentional to reduce footprint and to eliminate need for hookup wire between components. Only leads of components are used.
Notwithstanding the picture, which I couldn't rotate after inserting in post, the boards are mounted horizontal.
One further tip: don't trust the adhesive on the back of the LED strips. Install double-sided tape first. I have to go back and re-adhere some strips to car roofs.
Phil solves the "not enough power" issue ....
There are more TIUs and AIUs under the benchwork behind the Legacy controllers.
Given how cheap electronic components ahve become, and getting lazy in my old age, does anyone know of preassembled voltage regulators that will output 1 amp at 11-12 volts DC with up to 20 VAC input?
Thanks, Stan. I found the DC>DC and AC>DC units you referred to on the internet. FOund one source, in the US, that sells the DC>DC for 10 for $11.98 including shipping. A Chinese source has them for $0.80 each, which is cheaper than I can build them. Last time I ordered something from China (Aliexpress), it sat in "Singapore Post" for several weeks, which was unsatisfactory.
Still looking, but cheapest I found the AC>DC is 5 for $10 from Aliexpress.
They seem to have more components than the units I built, pictured above. I wonder what the difference is.
Your idea of a central DC rectifier is a good one, but of course for installing in rolling stock an individual rectifier, capacitor, and (for DCS) choke must be added.
Sorry if I missed it but instead of building your own boards have you check these out?
About 8-10 times more costly than home built.
Not to mention the 21-14 LED's I get in an 18" car distribute the light more evenly. The fact that I do it for less than $3/car is icing on the cake.
Still looking, but cheapest I found the AC>DC is 5 for $10 from Aliexpress.
They seem to have more components than the units I built, pictured above. I wonder what the difference is.
Do you have a link or photo of the $2 AC-DC. I could not find it on that website. If it a switching regulator circuit it will have more components than your linear regulator circuit.
The big win with switching regulators is conversion efficiency. Using your example of 20V in and 12V out at 1 Amp your linear regulator taken in 20 Watts, puts out 12 Watts. That's an efficiency of 12/20=60% with 8 Watts "wasted" going up as heat.
A switching converter would run ~90% efficient so that 12 Watt output only requires ~13 Watts of input with only 1 Watt wasted as heat. The practical benefit is you only draw 2/3 Amp from the 20VAC transformer (the linear regulator draws 1 Amp) so you can power more accessories.
Of course the efficiency numbers don't translate to big wins in passenger car lighting where the powers involved are 1/4 or 1/2 Watt.
Not to mention the 21-14 LED's I get in an 18" car distribute the light more evenly. The fact that I do it for less than $3/car is icing on the cake.
I like the "even distribution" from the strips too...thinking back to cars with glaring hot-spots from limited bulbs. Of course the "real" application for these 12V LED strips is for in-home under-the-counter lighting and the like...so smooth-even lighting is needed. It's curious that the strip spacing of the LEDs at 1:1 scale still works for even lighting in 1/48 scale passenger cars!
Stan:
Sorry, I can't find it this morning either. URL is below for 5 for 15. Let me know if this doesn't work. You'll have to get it onto one line
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