Battery static is 12.20 V.
IF "IF" you are measuring this AT the igntion switch IE the battery wire going to the switch, AND WITH the key in the "run" position, then the switch or the connector is your drop, or at least a whole big bag of it
To fully test this, round up a couple of male spade/ flag terminals and make a short jumper wire with no14 or so. Disconnect the switch, and jumper the switch connector from the red batt to the blue. Go out to the ballast and see if things improve