2 Quick Questions

Use a vacuum gauge to tell if you have a vacuum leak. All the auto parts stores will have them, cost is $17-$30 depending on manufacturer. A stock cam'ed engine will pull 16"-18" of vacuum at 650-750 RPM.

Finding leaks can be another story. Check all the hoses, especially where they connect to fittings for cracks & rotting. A squirt oil can filled with motor oil can be squirted on places like the manifold mating surfaces and the fuel injector mounting holes. Use motor oil since it will not flash fire like gasoline or solvents will. When you squirt oil on a leaky place, the oil will be sucked up and the engine will change speed.

Dump the codes and see what the computer says is wrong if you are stalling and have eliminated vacuum leaks as a possible problem.

Here's the link to dump the computer codes with only a jumper wire or paper clip and the check engine light, or test light or voltmeter. I’ve used it for years, and it works great.

See http://www.troublecodes.net/Ford/
OR
See http://www.dalidesign.com/hbook/eectest.html for more descriptive help
OR
See http://www.mustangworks.com/articles/electronics/eec-iv_codes.html

no light is needed for codes. additionally, some codes are stored (KAM) while never triggering the light.

some 88's (and earlier) gt's dont have a functional CE light (thanks Jrichker for help on that one a while back. no wiring to the light. some/many 88 and earlier ones dont have one from what i read in here).

those sites (Jrichker's links) are the best i have seen for codes. you can get a code puller for around 20 bucks at wally mart (but not here). for me, 30 bucks from autozone. some parts stores will pull OBD-I codes for free (some only do OBD-II).

read your repair manual too for code info. as i recall, you can use an analog voltmeter or test light to get codes (no CE light available).

good luck.

im sure Jrichker will have better ideas than me.
a quick test would be to remove the serpentine belt and turn the pulleys by hand. are any of them overly resistant?

im more inclined to think it is something with engine management. the whole changing idle characteristics while rolling a little sounds familiar (cant remember if it's the stang or eclipse that does that).
have you checked the components that relate to idle (tps, IAC, etc)? clean them up. lots of posts on doing it (search). between that (good idea none-the-less), and checking vacuum (your whistiling and falling idle), that should get it. at least in my experience. good luck.