the jumping
Jumping
Hmm... Now I'm not so certain. EHT arc-over produces impulse increases in deflection factor, which then returns to normal pretty quickly, till the next arc-over. Yours acts more like a bad connection, switch contact, fractured component, or flaky semiconductor.
I'd still say open it up and clean it.
Besides, if you open it, you might be able to pinpoint where the click sound is coming from.
Here's a good way to locate small repeating sounds: Get some flexible plastic tube, 30 to 60cm long, about 10mm dia.
Stick one end in your ear. Move the other end around in the equipment. It will become really obvious when you have the tube end close to the sound source.
It's like a stethoscope, only no metal parts.
This works for locating smells too, but via the nose obviously.