Ah ha! managed to fix it: AS-GT no power problem.

I had a quick look on the Cloudy Nights forum and someone else had exactly the same problem on their AS-GT mount as me, a faulty switch. So I used the same fix.
I soldered a small piece of wire across the switch to bypass it.
I'll see if I can replace the broken switch later, but at least for now I'm back in business.
Funny thing is when I buzzed out the switch with my volt meter/continuity tester, it checked out OK. It was only when current passed through the switch that it failed.
Must be quite a high current.