No, the fuel pump only runs while cranking the engine.
The harness for the ignition control module are a known problem and could cause a no spark condition. Both the ICM and ECU have test methods in the FSM.

Thanks, I am undusting my FSM to see if I can pinpoint my problem.

Hey dude,

If it does turn out to be your ECU, I've got a spare for a '90 you can have for like $20 + shipping. It's just sitting in my garage collecting dust.

Sending you a PM

Thanks guys,

88 red Montero with the Dakar Special Edition decals, 438,000 miles (As of 7/23/2012) some occational blue puffing but still strong and counting!!! I am going ppsshhh (turbo), Stay tuned =) ...