I went to the U of A (Tucson) in the 60's and 70's and I know how you feel about the desert. I lived in SoCal for 15 years before moving up to NorCal (Bay Area). I retired and moved up to Ukiah. I love this area.
:welcome to SDD JP. Tell us more about your truck, like year and model. Put these in your signature by tapping on your name at the top of the page and selecting Signature. Then fill it out. :)
4 amps will kill your batteries until you find out what is pulling the current. The Glow Plug Controller might be doing it, or the stereo or??? Does it always pull 4 amps? More or Less?
That fuel pressure if from the tank to the HPOP (High Pressure Oil Pump). The HPOP ups the fuel pressure to something like 3000 (three thousand) PSI or more, to the injectors. It sounds like you are GTG if the truck runs good.
The first truck I bought was a 1972 F-250 with a 4 Spd and power steering. No AC or power anything. I was shocked when I saw the Out-the-Door price of $4,040.00 and 46 years later they are going for $100,000!
These engines are known to surge when cold starting. This is due to the oil, 15W 40 is what the factory puts in. I changed to 5W 40 and the surging went away. I have never heard of the alternator causing surging.
You can use the wiring on the tow plug (4 wire or 7 wire) to get to the brake lights but these have blinkers tied into them. The third brake light in NOT in the tow wiring, as I recall.
What are they telling you? Are you getting anything for your non-use of your truck? When do they think it will be put back together? I am stating nothing specific to the 6.7, just want to know more relevant information. :)