Engine will not crank?

I've copy and pasted some of the information from my previous thread:

I was finally able to get the battery fully charged again and tested over at AutoZone & they say the battery is good. I'm getting about 12.65 - 12.69v from it.

I removed, cleaned, sanded and reattached the ends of both the (+) and (-) battery cables to ensure good connections.

I then checked for the voltage from the battery-side (+) end to the connection on the starter & that is 12.63v. I also put the (+) lead from my multimeter on the (+) connection of the starter and the (-) lead of the multimeter on the starter body and got about 12. 60 - 12.65v.

I've already had a "hot shot" installed on the truck due to the well-known issue of needing 12+ volts running through the ignition switch in order to engage the starter & the consequential voltage drop that occurs from having to go through so many points. Also, it wears out the ignition switch. That's not it. I never had a strong, solid start consistently (sometimes yes, sometimes no) but after the hot shot installation the intermittent no-start went away.

I tried turning the engine once and heard a click immediately followed by the starter engaging. For about a half second before shutting off and everything went dead. I then immediately turned the key to ACC and still got dash lights.

Then I did the previously mentioned cleaning and reattaching and tried again. Same thing, but this time when I tried the get lights again immediately afterwards it was like the battery was dead again.

So, in short:
-sometimes I get lights, a click, and the starter attempts to engage
-sometimes I get no lights, no click, or engagement from the starter
-sometimes I get lights and a click (this happens most often)

I was able to rotate the engine just fine with the spark plugs out (that's how I discovered the coolant coming out of the #2 plug hole) but couldn't get it to move with the plugs in. Don't think anything is locked up internally.

I also put one lead on the (-) battery terminal and one at the starter relay and get from 12.57 - 12.41v when I turn the key to start.

I guess next would be to remove the starter and attempt to bench test it & make sure it has good ground to the engine block? I'll try tapping the solenoid area before starting the engine again tomorrow.

Update:
Okay. I tested the trigger wire's connection through my hot shot (pictures included). I wasn't sure which wire (white or blue) was for the trigger wire since they're connected inside of a split loom that I didn't want to risk peeling back/off, so I tested each wire.

The blue one would give a reading of 0.01v when I turned the key to run.
The white wire would get a reading of 11.40v.
The battery has discharged a little, so I put it back on a trickle charger.

Unlike on my previous attempt where the starter would attempt to start then nearly immediately stop, this time I heard no cranking sound whatsoever (just a click) any of the times I tried to start the engine.

The photos are of the hot shot that my starter is wired into - there are additional photos earlier in this message string.

The video is of my turning the key to RUN with the lead on the white wire's location of the hot shot relay.

This relay was installed to bypass the long-distance voltage travels in the original, factory wiring that eventually causes intermittent starting issues solely because not enough voltage makes it to the final location to initialize the starter and/or the contacts wear out and pit. I think I also mentioned this in a previous post on this thread. Happy to explain more if needed.