What do you mean the car completely resets?
It sounds like you may be having a similar problem as I am. Which my problem I believe lies with the alternator. When I come to a stop, my car idles just fine but the voltage will drop to 12.3v for a few seconds and then go back up. As if the alternator shuts off for a period of time.
This may be normal, could be a possible shut off point for the alternator to conserve the engines power and save gas while idle I dont know, I know thats a little far out there for mid 90s technology.
All of the above things (braking, high beams, blinkers etc) use a bit of power, so as soon as you put on your brakes or flash your beams your pulling a bit more power from the electric system than usual and perhaps the alternator is not compensating for that and its causing a bad voltage drop. Which if thats the case, you need to either repair the alternator or replace it. It would most likely be a fried voltage regulator.
I suggest getting a volt reader to plug into your cig lighter to monitor voltages at all times while driving, thats what I did. Only cost $20. Or you can rig up a multimeter if you already got one.
Most of the wiring in these cars are a laugh, so it wouldnt surprise me that most of the electrics would start to fail prematurely.