why won't it stay running?

sounds like the ignition control switch to me, its under the steering colum on the right side, it has a bunch of wires going into it, they are notorious for going bad. will cost ya about 30 bucks at autozone

I don't know if Ford still does this, but they might.

On the old points-style ignition systems, they had two feeds for coil power, one for start and one for run. During starting, the ignition was fed a full 12V and when the key came back to run, it was fed through a resistor wire that dropped the voltage down to around 9V. It supposedly helped extend the life of the points. This is alot like the ballast resistors used on Mopar stuff throughout the years.

I had one of those wires burn out on me once and I just about went insane trying to figure it out. I ended up talking to a guy at the Ford parts counter who'd been around for years and he told me about it. Replaced the wire and everything was fine. Well, except for my sanity.

I went looking for a wiring diagram, but gt350r's site is down. I was hoping to confirm or deny my theory.

Yes the switches will interchange.