Just take the starter out or check it out with a light and crank it and see if the bendix is pushing the gear out, if so starter is good and wired up correctly, Keep this in mind...In 93+ they used different starters, (PMG I believe they were...permanent magnet starters, much smaller and were wired differently than the 86-92 stangs). Using a 93 starter on an older stang is kinda considered an upgrade since they're ALOT lighter and smaller (nice for header clearance) and supposedly have more torque. On my 87 stang and up till 92 there was only a Thick Red wire going down to the starter, (that's what you have right?) the current was controlled via the solenoid on the fenderwell and was only live with the key in start. On the 93 and up stangs there's a thick red 12V wire going to the starter LIVE ALL the time AND a small ignition wire to engage the solenoid ON the starter to send the live 12V to the starter to crank AND power to the bendix to pop the gear out. What I'm getting at is in 86-92 years as soon as the stud coming out of the starter got 12 volts it would automatically pull out the gear in the starter AND turn the starter on BUT with a 93+ starter the solenoid On the starter controls the gear to come out. SO it could be that you just hooked up the RED cable to the lower post (there's 2 right?) on the starter (which will only turn the starter over but not bring the gear out). If this is the case which I think it is, you will need to bring down the wire from the push on connector on your fenderwell solenoid and bring it down the solenoid onto your 95 solenoid on the starter (there was a little length of yellow wire that came with the 95 starter right? if not there's a little male connection on it you would hook it too. )and put the thick red wire you have going to the starter on the other post on your fenderwell solenoid.
Let me know what you find out and good luck