BBS01b Controller: Why is there a current when battery is disconnected?

[Nealh]

Now that I have those two motorcycle lights wired to the battery wires via a switch, they flash on very briefly after the battery has been removed, and I turn the switch on. It's a complete discharge, doesn't happen again with subsequent activations of the switch. I recall getting a small shock before, from the old controller - but the short circuit between battery connectors (damaged insulators around wires - a knick or melt?) or it was that trash power module killed it.

You had the answer early on in the thread, the controller has a large capacitor on the inlet side which will hold a charge for some time, turning the lights on will momentarily drain the charge and then not again until the battery power is connected again.