To clarify some stuff.

Your first note talked about a voltage drop after 2 seconds -- that's about the time that the fuel pump is shut off on startup. ( It runs for 2 seconds then the computer shuts it off until it senses that the engine has started).

So, you might have just been seeing your voltmeter drift downward.

Your battery voltage does seem a touch low - although not horribly so.
Full battery charge under controlled conditions is 12.65 v. However, temperature is a factor. Also, some DVMs aren't all that accurate.

You might try checking your charge voltage. Leave the meter on after the truck starts and see what it goes to. 13.8 v is pretty common, but it does vary. Could be that your alternator is not quite up to it.

Could also be worthwhile to make some jumper wires so that you can monitor battery voltage from the cab. Use some ring tongue terminals and try to sneak the wires into the cab with some kind of a connector in the cab so that you can get a reliable connection to your meter. Then you can see what's going on when it fails.

Good Luck,

hj