battery draining rapidly without anything switched on

I have a XJ 650 4KO 1981. I had the motor apart last year, and it started, but ran badly. I have just got over a bit of an illness, and picking up where I left off.
1 - the battery had deeply discharged, dried up an declared deceased.
2 - On testing the circuits with the new battery, I found the battery draining rapidly without anything switched on
3 - By process of elimination, disconnecting at the fuses, I found the current drain stopped when I disconnected the big multi (7) pin plug at the reg/rec.
4 - A car mechanic friend suggested the alternator to be at fault
5 - I did notice a wee spark when I pulled the connector apart
6 - I just remembered the lights being dim/yellow last year when I tried them to see if they were working
Has anyone had/fixed a similar issue? - (I have done a search, but I am not very good at that type of thing)
Thanks