First thing you need to do is test fusible links with a meter. They have a flameproof silicone jacket, so they will "look" good, but can be severed internally.
Are all the bulbs specified good, or are you being led down the primrose path?
Are fuses installed and good? Again, check with a meter...
In your first picture, the two left hand Phillips screws are the ground for the dome light. They're ground is created by screwing into the roof. If the screws are not tight to the roof, or not making good contact with the two traces on the left, the lamp will be intermittent.
That's going to be part of the HVAC control unit and blend doors. I would contact the used part dealers on classifieds forum and try to pick up the entire assembly as opposed to playing games with the one that has been hacked up.
The 2 connectors on top of the transfer case are for switches that indicate low range and neutral. They have nothing to do with vehicle speed sensors.
What does the FSM for your truck tell you about a flashing OD lamp?
The dome lights and gear selector light are 2 separate circuits, fed from 2 different power sources with 2 separate ground paths.
All dome lights recieve a constant +12 from the 10 amp DOME fuse in the relay box on the left fender. The lights are triggered by grounding one of the door switches...
I went back and re-read this thread and I am a bit confused. Let's go back to the beginning. Please answer yes or no to the following questions:
Is the starter cranking the motor at this point?
With the key in the ON position before cranking the starter, do you have the CEL and CHARGE lamps...
Yea, I kind of rolled my eyes as well, but decided to let @CharlieS make the decision based on his skill level. Good soldering skills take time to develop, just like anything else. After 4 or 5 thousand you get pretty good at it.
In the last 40 years I've never had a solder splice fracture, but...
You will get several answers. I prefer solder with heat shrink, but I've been working with soldering irons since the 1980s. A bad solder joint is just asking for trouble. If your skills are questionable, then crimp connections are better, but you need a good crimp tool to ensure a proper...
All of the original hardcopy FSMs have an index page. All of the digital FSMs are bookmarked according to the hardcopy indices. The advantage of the digital ones is that you can search on a keyword within Acrobat.