1988 Sierra: every now and then motor won't start

[RayInAlaska]

I have the following problem with my 1988 Sierra GMC, 350 TBI motor, with a 5-speed manual transmission:

Every now and then (maybe once every other week) when I turn the key the motor won't start. It acts as if there is no power whatsoever going to the starter. The only noise heard is from the fan, and the gages and warning lights as well as the interior lights (if I have the door open) turn on normaI. Even the headlights turn nice and bright if flip the switch. But the starter solenoid does not click nor makes any noise whatsoever. If I remove the key and let the truck sit there for 30 minutes or longer, then it starts as normal. The battery is good (passes a capacity/discharge test).

The problem may happen after I park the truck after driving for a while and the motor is warm, but it may also happen when the motor is cold a few hours later.
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I have thought that perhaps the clutch safety switch may be malfunctioning, or that the starter may be going bad. So a couple of days ago I replaced the easiest component, the safety switch, but the motor failed to start right after. I let it sit there for a couple of hours, and then it started without any problem.

Have you had a similar experience to mine with your truck? I am trying to isolate the malfunction to as fewer components as possible, and can't think of anything else that may cause this problem.