2000 Chevrolet Silverado 5.3l when stopped in gear my voltage drops to 11amp and starts ruff idol. When I start rolling amps jump back to 14.5amps. When in park or neutral its fine. Only other problem is low idol sometimes 400 and knock sensor bank 1 shows confirmed.
I would check your battery terminals, just because they are tight, doesnt mean the tabs under the side connector are in full contact with the battery terminal.
Also check for corroded ground connections.
Just a fyi, the 14.5 would be DC volts.
Does this happen more with your foot on the brake? What about with the headlights on?
Using a DMM, connect to the battery and when it's idling, turn on the headlights, then high beams, then rear defrost, also move the power seat or turn on the seat heater.
Watch the voltage and see if it can maintain I believe 13.4 or 13.6 minimum.
I'm suspecting your alternator right now, even though your red charging light may not be illuminated. You may have enough to keep the light from coming on, but not enough to keep up with the acessories. Your engine will likely run rough with low voltage output.