The following information is presented subject to the disclaimer that
follows it.

Sounds like a leaking (or hanging) fuel injector. My 96 did this. Hook up a
fuel pressure guage to the Schraeder (sp?) valve on the fuel rail near the
firewall. It should hold pressure for quite some time (20 to 30 minutes)
after shutdown. On mine it did sometimes, but other times not, requiring
multiple repititions of the test. After I saw it drop in a hurry once, I
took the fuel rails off with the injectors still attached. By cycling the
key I was able to pressurize the injectors. Then I applied test leads
between the battery and the leads on each injector. All sprayed when power
was applied and had good cone-shaped patterns. One of them however, didn't
stop spraying when power was removed. This was a BAD THING. When this
occurred, I would get the same result as you - immediate restart OK, because
the fuel hadn't all leaked into the cylinder yet. 10-15 minute wait to
restart no good, because all the fuel was in the cylinder, essentially a
flooded engine. 30+ minutes OK, all fuel evaporated. I replaced the
injectors with 24 pound Ford MotorSport injectors from Summit Racing and the
problem went away.

Within six months of all this I had the opportunity to trade for a 2003 Z06
and did. The 96 was running fine until the day I traded it.

Warning and Disclaimer (especially because in an earlier post you stated
that you were an idiot): Gas is flammable, and batteries and electricity
make sparks. Gas, betteries, and electricity should only be used by a
competent technician. If anyone does any of the thing I have listed above,
they do so at their own risk. This post outlines my experience - your car
may or may not have the same problem.