Update:
I carried out the following tests last night to try and close down the issue:
A. plug the TM13 into the socket next to the dodgy socket.
B. Move the TM13 nearer to the main fuse box.
A. that operated lamp 2 (the one I couldn't get to operate), but lamp 1 (that worked yesterday) stopped responding!
B. that operated lamp 1, but not lamp 2!
I tried the TM13 in various sockets and eventually found one that operated both lamps. I tested the original lights and they also work OK.
Still no idea why - but it works.
I will try and solve the SC9000 problem next.
Frank