A little progress.
This has been an intermittent problem that seems to come and go at random, or to get progressively worse, then stop all together. So this morning when the truck wouldn't start, I decided this is my chance to dig into the issue while the problem is actually happening. This is the first time I've been able to test while the problem was occurring, and as such, I think I found something.
I pulled the ignition wire from the relay off the solenoid and tested for voltage, and I got 12v when I turned the key to start. So then I put it back onto the solenoid and began looking to the other connections at the starter. So I touched the base of the spade connector with the meter probe, and this time I got no voltage. So I tried again with better lighting and at a better angle. No voltage. Then I pulled the wire off and unwrapped it to check for damage. Nothing seems out of place, but just a few minutes after I got that first positive result, I'm not getting any voltage at that ignition wire no matter what.
The relay behind the fuse panel does click on and off as expected, but is it possible that the relay is still bad, even if it is physically actuating? If so, is this a special relay, or could I open that panel and simply replace it with a matching type from NAPA?