Check out Fig 2 on page N3 of the workshop manual. It pretty clearly shows the battery box drain going to the hole on top.
I can't find the reference at the moment, but I'm fairly certain that the factory routed the OD wires on the TR3 through the hole located low on the LH side of the tunnel. I don't like that location, so mine are routed out through one of the holes in the vertical part of the firewall, and go back to the switches & solenoid. That way I don't have to mess with the wires when R&R the tunnel. (Got the idea from Triumph, that's the original routing on Stags.)