I'm not a quarter smart enough to give exact details to this, my electronic skills are mostly visual. BUT, I think I have seen your 4-prong combo flasher before, there should be a small switch of some sort, its controlled by a strip of metal and two electromagnets, so the strip flops back and forth, I can't explain it but you should be able to move the magnets closer so the response is slower.
This method is used for the really old switches, I doubt it would exist on a 96. It sounds like there is a short in the flash circut that is making your low-voltage thingy go off. So if the system thinks there is a light out, find the incompletes of the circut and solder them togeather or ground them, it should make the flasher think the lights got replaced.
Hope that helped, if it was just crap advise, let me know and I will be sure to never answer questions about flashers again
Peace.