Im going to try again to resolve this starter issue. This starter circuit is very primitive, any more primitive you would have to use a rope or a hand crank and that is good. If I am correct you have a 96GT or cobra wiring loom. As far as I know, a mustic cobra is just a color, not a performance package.
You say you can fire off the starter by squeezing the relay that is good, the wiring to the starter is intact.
I am going to assume that you checked the white with a pink wire at the ignition switch for power when you turn the ignition switch to the start position. It should have power whether ot notthe clutch pedal is pushed in or not.
It would appear that you may have a relay control issue on the white with a pink stripe pin 85 or the black ground wire pin 86 of the starter relay.
THIS CAN BE CAUSE BY 3/4 THINGS
Check for power at pin 85 of the starter relay. Use a test light, if the light glows when you step on the clutch and turn the ignition switch to crank, this is good.
*Don’t use a cheap 30 cent test light, use headlight bulb or something that can draw some amperage.
If the light does not glow at full brightness, refit the starter relay and test the clutch pedal position switch.
Clutch pedal position switch- a gray 2 pin/wire connector under the dash with a red/light blue and a white / pink stripe on the other side, if you think the switch may be faulty, short these two wires together. Does it crank now if so replace the CPP switch.
Test pin 86 in the fuse box for a good ground, use the test same test light, BUT hook the test light up to the positive side of the battery. If the light turn on as soon as you probe the terminal, this is good.
If you have no power to pin 85 of the starter after shorting out the CPP switch, and you have power coming from the igniton start switch:look in the left hand side of the trunk area of the wiring loom.
Look for a black box, (not a white one, I believe the white on is for the locks)that has a white or gray connector on it. If the box is missing look for the connector. Look at the back of the connector to find a white with a pink stripe in one row and a red/blue stripe in the next row over.
This may help the white/pink wire will have no wire on either side of it. The red/blue wire will have a black with a green stripe on one side of it and an open space on the other. Short these two wires out, does the car crank, if so problem solved.
If not we can go further, test the white /pink wire for power when stepping on the clutch and turning the key to the start position. You should have power.
Lets see what happens when you perform these tests.
Don’t confuse pats with anti-theft, they are not related.
Remember this circuit is primitive, so you only need test a lamp and/or multi-meter.
Good luck. Let me know.