You might check the 'common' (or ground) path for lighting in the caboose. I'm referring to the path from the outer rails, through the wheels, truck frame, attachment to the metal floor, wire or other path to the bulb socket, etc.. Sometimes loose or painted joints in this path can be as blinking-problematic as the more common center roller path to the bulb.
A problem such as yours drove me batty on a restored passenger car (single bulb). After focusing my efforts to improve center-rail pickup...with no satisfactory resolution...I decided to check the common path. Turns out the restorer had repainted the metal floor...rather heavily, in fact...and had not removed the paint around the bearing surfaces at the truck attachment points. I used a small pencil-shaped wire brush (MicroMark) to remove the floor paint, brighten the floor and truck bearing surfaces. Bingo! VAST improvement!...Not 100%, but way better.
In the end, besides keeping electrical paths...all points rails-to-bulbs...clean (a periodic maintenance requirement just as with oiling/lubricating bearings/gears) I've decided the other possibilities for this sort of problem are:
1) Increase redundancy in the electrical paths...e.g., additional center roller pick-ups.
2) Use on-board battery power. (Not very convenient or practical)
3) Convert to aftermarket lighting (typ. LED's) that features an inherent 'keep-alive' capacitor to eliminated the blinking problem altogether.
Just some thoughts on the matter.
KD