The monitor should show correct battery voltage, regardless of solar panel input. Even with zero solar panel input, the monitor should display what is actually in the batteries.
Since you say the actual 12V system appears to be functioning fine, I would suspect either a faulty monitor, or a bad/corroded connection between the monitor and the batteries. Typically the monitor is a separate component from the charge controller. Measure the voltage at the controller. If the voltage is normal there, then check connections between the monitor and controller. If everything seems normal there, a faulty monitor is likely.
Casey
1995 K1500 Tahoe 2 door, 6.5LTD, 4L80E, NP241, 3.42's, 285/75R16 BFG K02's; 1997 506 block; Kennedy OPS harness, gauges, Quick Heat plugs, and TD-Max chip; Dtech FSD on FSD Cooler; vacuum pump deleted, HX35 turbo, Turbo Master, 3.5" Kennedy exhaust, F code intake; dual t/stats, HO water pump, Champion radiator; Racor fuel filter