The buzzing is probably the starter solenoid, usually due to a flat battery.
The rev-counter is an electronic one driven by pulses from pin 15 of the igniter. The only thing that I can think of is that the buzzing, which is due to the solenoid coil energising and de-energising, is sending high voltage spikes into the electrical system due to the back-emf (counter electromotive force) generated in its winding.
A forum community dedicated to Triumph Motorcycle owners and enthusiasts. Come join the discussion about performance, racing, cafe racers, bobbers, riding, modifications, troubleshooting, maintenance, and more!