Well, like i mentioned in a previous post, when the gauge isn't working, the alternator isn't being charged, you had a freshly charged battery, and the truck will run fine for awhile until it dies out below what the computer needs for it to run.
Now your problem, in my opinion, is going to be a wire shorted, flat out somewhere, you haven't looked, or missed it. I told you earlier that mine has this same problem, and i believe mine to be behind the motor somewhere, and luckily i have moved my harness around enough to where it doesn't short out, popping my fuse, hasn't for a few months now at least.
I know it's still a problem i will need to address, but until mine starts acting up, not gonna worry about it.
You're going to have to seriously start tearing apart the wire looms on the engine area, and especially behind the engine area. I recently had to repair a wire on a friends Suburban for a similar issue, it had rubbed through and was causing a different sort of issue.
get back behind the motor, grab the damn harness, move it around pretty good, and then replace the fuse, if it pops, move the harness some more in different areas till it DOESN'T pop. When you hit the gas and the fuse pops, it's because the motor moved, grounding out the bare wire.
BTW, removal of the hood makes for a MUCH easier access to all the wiring under the hood, and most of it behind the motor block.