What kind of regulator do you have, Sean? Is it the OEM version or some aftermarket thingie?
If OEM, unplugging the Green wire releases the 'relay' contact inside, letting it spring upward to connect to the HIGH CHARGE contact. (In other words, this is the 'fail-to-safe' mode if the relay coil were to break open a wire inside.)
This all said: the OEM upper contacts can (and I've seen quite a few that do) get burned after 50 years of spotty use. This reduces the amount of current that gets delivered to the field coil to (try to) increase alternator output. They also can get corroded: this causes similar, but intermittent, hi-charge mode - often after the bike sat a long time. What happens then is: when it switches to HI current mode, the contacts don't connect very well (or at all) and then the output from the alternator drops way down - even to zero, sometimes only momentarily (or minute-tarily), and then it suddenly appears to start working again. This is caused by visible crusty spots (usually white colored spots) on the surfaces of those contacts where they meet.
I've polished these 'spots' off with points files, emery paper, and even the little nail file in a Swiss Army pocketknife. The latter is hard to get in between the contacts, as they are only about 0.2mm apart.
If the relay is an aftermarket type, I don't know enough about what you have to try to help at the moment?
In the 'old days' the chopper builders who installed the [in]famous dual-rectangular-headlights (one above the other on the triple tree) would just jumper the Black and White wires together, period. Since I was in Illinois them days, and the headlights had to be ON all the time there, this made some sense - but it did also dry out the battery pretty quickly, and every winter we had to replace the little bullet connectors (Yellow wires) where the alternator plugs into the harness at the left-side tranny cover. You can get to them by removing the sprocket cover for inspection, tricky to replace them, though, because they are on a short leash with the tranny cover installed.