Step 1. Verify your gauge with a multi-meter.
Step 2. Measure voltage drops with mult-meter.
Use a volt meter (multi-meter) to measure from (-) battery terminal to the engine where the (-) lead connects. If you find more than a few tenths a volt it could be the ground cable, or connection at the battery. Also check from the (+) terminal of the battery to the alternator output, again only a few tenths is good. Since it starts out at 13.8V, I assume your alternator is working. Now you can take this a step further and measure voltages on the interior side of the bulkhead, referenced to the (+) battery terminal. When you find about a one volt drop you may have found your problem.
Danger!!!! Keep meter leads and fingers away from moving objects like the fan and belts.