sometimes charge sometimes dont :(

[roncoinc]

Noticed engine didnt want to turn over and a big voltage drop.
had battery tested,said it needed a charge.
charged it and hardly drops a volt turning over now.
hooked up dvm to battery and took it for a ride.
batter static charge was 12.77 , running voltage went to 13.75 or so.
then voltage dropped to 12.77.
shut off and restart and back to 13.75 for a few feet then drop back down again.. WTF ??
volt regs are cheap enuf but i'm not sure that is it..
also reg has wires going to a small box bolted to the bulkhead,,what is that for ??
in pic "A" is the three terminal volt reg and "B" is the part i question what is ?
suggestions ?
tnx..

[Spicyunicorn]

Trace the green wire coming out of starter generator make sure it doesn't have a loose connection or any visible broken spots