If you have fixed voltage bus wires for accessories, the easiest thing to do would be to connect one wire from each flashing light to the "hot" accessory bus and the other to the common ground bus (or you could use one of the outer rails on your track). If you want to control the light, you can add in a simple on-off switch to turn the light off.
The 154c contactor uses the weight of the train to make the lights on the 154 flash, so it is understandable that lightweight cars (especially those with plastic trucks) are causing trouble. True you can add weight to the cars, but the best thing to do would be replace the contactor with a modern circuit flasher triggered via an insulated track section. I'd recommend the #367 flasher from Dallee Electronics, which will permanently solve the flashing issue. The last published price for the #367 is $24.95.
You can also manually control the signal with a momentary single-pole, double-throw switch (on-off-on), but to get the lights to flash you would have to rapidly throw the switch back and forth. The Dallee part would automate this for you.
-John