Questions; have you replaced the actual electrical part of the ign sw? It is under the dash bolted to steering column. Have you gone through the starter wiring diagram starting on page 8A-30-0 in 95 service manual? Get manual @ My Files
The chain of events that cause starter to turn engine over start with turning key to start position. Rod links key to electrical part of ign sw attached to steering column. Yellow wire from elec ign sw goes to a splice S223, where power is split. 1st lead from S223 goes to points of theft deterrent relay (TDR) on yellow wire.
2nd wire from S223 goes to transmission position switch, or clutch start sw, depending on which trans you have. If switch is good, power goes to coil of theft deterrent relay (TDR). Next step involves vats security system.
If key sends proper resistance to the theft deterrent module (TDM), then TDM will supply ground to TDR coil. Electra magnetic field will form closing TDR points which transfer power. Power goes to starter on purple wire.
Now that you know how system works, you can either troubleshoot the problem, or wire in push button starter switch.
The push button starter sw is actually simple. You can get a push button momentary sw at most any auto parts or hardware store. Get 1 that is rated 20 amps or more.
You have 1 wire connected to positive terminal of battery. It goes to 1 side of the switch you just bought. The other side of the switch will have a wire that connects to the starter solenoid where the purple wire connects. You don't have to disconnect anything.
This way, when ign sw is behaving, you can use it to start car. If ign sw doesn't do the job, you can use the start sw you just put in. Nothing is hurt with both switches in the circuit.