Cadillac Repair: major issue???, electric fuel pump, cadillac eldorado

Question
Hello again Tom,
  I have been dealing with this new car I got, It is a 1983 Cadillac Eldorado Biarritz.  It has 56,000 miles.  4.1
fwd V8.  I bought it after it sat for a while, when i got it home it was shifting funny.  then after driving on the highway for bout 30-45 mins it will backfire and sputter and eventually die.  I talked with you about a week ago and was thinking possible CAT, after changing the cat the problem still exists.  I then thought that my clutch fan was bad so I changed that.  It did help a little bit, made the problem take longer to happen but it still seems too get hot and want to die.  The stop engine temp light will not come on while running but if I put the key in the ignition while the engine is off it will come on.  I haven't changed the cap/rotor/wires yet.  Was thinking it may be either; Thermostat/ignition(cap/rotor)/water pump/possible timing?  I don't know where to start.  When driving home i get almost home and have to let it rest and (cool down?) before I can go again.  Other wise when it's cold it runs like a top.
The only code it has thrown was 39 which I asked you about and that is the TCC system.   Ever heard of something like this happening before.  The EGR looks new?  In need of help!
Any help would be great Tom thanks.
Robert Johnson

Answer
When it dies, Check to see if you have fuel pressure and if BOTH fuel injectors are spraying fuel. Also check for spark at the spark plugs during this fault.

Possible faults:

Ignition module getting hot and shutting down.

Fuel pump getting to hot and shutting down. See if it makes a difference if the fuel tank is FULL as the gas is what cools the electric fuel pump in the fuel tank.