Could well be a dying battery. At 11.9 volts it's down a bit from where it should be. Since voltage comes up when running, charging system appears to be OK. You should be able to get both the battery and charging system tested for free at any McParts auto store.
My personal experience is that MBs can do strange things when the battery is on its last legs. My spouse killed the giant Diehard in her diesel wagon late last year by leaving the headlights on for several hours. Even after jumpstarting the car, many strange things happened. ABS and ASR lights on, A/C compressor engaged with the climate control in economy mode, even an occasional phantom windshield wiper stroke. Replacing the battery with a fresh one banished all the ghost problems. Strange but true.