Wouldn't start - Help

[Grahamm]

It sounds somewhere near the battery, [...]
The battery is 26 years old original to the bike and is kept on a trickle charge. 

I'd suggest putting a Drop Tester on the battery, because after all that time, it's probably dropped a cell and you're not getting enough Cold Cranking Amps.

The buzzing is most likely your starter relay: When you press the button, the relay latches so current can pass through to the starter motor, but that pulls too much power, so the relay unlatches, meaning there's now enough current to latch the relay again, but...