Engine dying after 20 or so minutes running

New to this forum and need some help. My son has a 1991 "Interceptor" boat with a 350 chevy engine, 2 bbl Holley carb, and Volvo Penta drive (not sure about the drive model). The boat cranks and runs fine for approximately 10 to 20 minutes under load, then fades out and dies. It acts like it's running out of fuel but we're getting plenty of fuel to the carb. Once this happens it will crank right up, but once you put it in gear it will idle, but when you try to give it throttle it will fade out and die again.
We discovered that when you turn the key on, the fuel pump will not come on sometimes. You can turn the key off and back on and it will work. We also had the problem of the engine not dying when turning the key off, it would continue to run as if you never touched the key. Once again you could turn the key on and off a couple of times and it would finally turn the engine off.
I suspect the problem could be one of three things.......................the ignition switch, coil, or the module inside the distributor. It doesn't have points and condensor.
He's had this boat in three different shops and none of them have been able to cure the problem. For one thing none of them checked the problems he described, they worked on the fuel pump but did not test the boat under load.
Any help will be greatly appreciated.

Not a coil problem, not a module problem. Start by checking the ignition switch. Next, there is a diode in that harness, that if it fails will keep theengine running, although, when diodes fail, they fail and no amount of switch jiggling will likely change behavior.

Thanks Sandkicker, I appreciate the advice. I have a brand new 600 Holley carb that I'm going to replace the 2 bbl Holley on the engine with. I also picked up a new ignition switch we're going to install today. If the problem still persists......................where would I locate the diode you mentioned in the harness?