It seems like grounds are always the curse (and not just on LBCs either - I was helping a friend troubleshoot some really weird electrical voodoo going on with a Chevy pickup, a bad ground at the front turn signal lamps was causing the whole dashboard to go dark when you hit the brakes or some kind of weirdness like that - we grounded that fixture and everything else worked correctly). I added ground wires to every bulb holder on the turn/brake/lights fixtures of the MGB I'm trying to reassemble. The sidemarker fixtures already had one (and the headlights always have a ground in their connector), but now all the external lamps do. And now all the lights work correctly.
When I replaced the positive battery cable, I added extra layers of shrink wrap where it passes thru the clamps below the floors and where it makes the turn below the battery box just to be safe. I also intend to either add very upsized grounding cables between the body and the engine, or just run a high-gauge cable from where the negative battery cable attaches to the body all the way up to a starter or bellhousing bolt to ensure there is a proper current flow both ways.