Strange problems with my GN, experts needed....

Bad ground???

You said the FP relay was hot. You may have a loose ground or poor connection to the relay. This would cause the FP to cut off and come right back on. When the connection gets hot enough it would disconnect, when it cools, it would reconnect. If it only will cut off when it's hot outside and not at night, it's going to be hard to find. I would suggest changing the relay if it hasen't been changed yet. Clean all that black gunk off. Use dialectic grease to keep it from corroding. Also check the plug at the tank for corrosion at the terminals.
I did a Hyundai that had almost the same problem as you have. It turned out to be the in tank FP body had to be grounded. Not grounded from the factory. Still don't know why it worked, but it solved the problem.
I would still see if you could swap out the spark control unit from under the coil pack. Heat will cause it to brake down sometimes. Check the grounds. Most problems are due to bad grounds.
I just thought of something else. How's the charging system??? Bad diode in the alternator can sometimes cause all kinds of strange problems with the computer.
 
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