problem

This falls under 5.0 tech.
Thread moved.

when it shuts off do you still have spark and fuel?

You may be the victim of the previous owners efforts. Poor workmanship or sometimes plain old stupidity is often one of
the causes of problems with EFI to carb conversions. For that reason, it is best to avoid them.

First, determine what distributor you have: remove the distributor cap and try to twist the rotor. If it does not move or
moves very little, you have the orginal EFI distributor in the engine. This is not good, since there is no spark advance built
into the distributor. The proper distributor is an 85 Mustang 5.0 distributor since it will have mechanical advance and a steel
gear compatible with the roller camshaft. Crane makes a really nice distributor for non-EFI applications.
See CraneCams for more information.

If the rotor moves and springs back to its original postion, you have a distriutor with mechanical advance. That is good,
since it is what you need. Since your problem gets worse as the engine warms up, the magnetic pickup in the bottom may be going bad.

For Duarspark wiring diagrams, see My 1960 Falcon
or
Carbed Ford Message Board :: View topic - Duraspark Wiring Diagram

or for much more , see Google (Google is the first place to search for stuff like diagrams and drawings)

duraspark wiring diagram - Google Search
for more help.