Buzzing from clocks when main beam is switched on?

[Falcon 269]

I hate electrical problems but I'd start by looking at every wire you worked with in trying to hook up the gear indicator.  Your problem sounds like a wire part-shorting to earth, a bad earth or possibly a damaged/mis-seating contact in a connector block.  It's not unheard of for one of the small prongs in a connector to bend or otherwise get damaged. 

Close inspection and logical re-tracing of your previous work should solve this.