Since it is fuel injected, rapidly pumping gas pedal to keep it running means it is lacking AIR not fuel.
All the gas pedal does now is let more air in it doesn't control fuel, computer does that using the MAP sensor on an '88, MAP sensor detects air flow.
My first guess with the soaking of the engine bay would be a problem with the TFI spark system, these are troublesome at this age, 20+ years old.
Good read here on TFI testing: Ford EEC-IV/TFI-IV Electronic Engine Control Troubleshooting
When engine is cold computer will run it with Rich fuel mix, so a hot spark is needed, a problem with spark system could cause a flooding like start up so adding more air, i.e. pumping gas pedal, would lean it out enough for weaker spark to ignite fuel mix.