Vintage tube amp resurrection with Variac?

That paranthetical bit should be factors of twenty and ten, not ten and five. Hit the Submit button when I should have hit the Preview button!

Don't forget earplugs and safety goggles.

I have done this a few times using this technique. There are different opinions out there, but an excellent audio technician told me this is what he did, and never had a problem, so that was good enough enough for me. Make sure you have speakers or load resistors on the outputs. Not having a load on the outputs could cause a serious problem. Also, watch the tubes as you increase the variac. If there is a major bias issue, the plates of an output tube may start to glow red. If this happens, definitely stop the process, as it will be best for a technician to take over.

@OP, I'm not a tech and that's what makes my post worthwhile.

Knowing what I DO know is enough to say that rather than screw around with your old amp, I'd have it looked over by a reputable tech. If the manufacturer is still around... even better. I bet the old PS and coupling caps are dried out and need replacing. Other parts may need to be replaced too. Here's a quote from TLS49's article:

"You should probably consider replacing the capacitors on an old piece of equipment even if it doesn’t hum. Old filter caps will fail sooner or later, so you may save yourself some time and trouble later on."

Seems like good advice to me.

I'm bringing back Fisher, Marantz, HH Scott, McIntosh equipment brands that are up to 40 years old vintage.

With tubes inserted that I'm confident that are good I connect several voltmeters connected to each bias pot or resistor to make sure that none of tubes will significantly drop or increase bias current during voltage increments. There's a slight risk of damaging tubes, but it's part of business give or take. Blind replacement of DC supply caps (assuming they're all bad) before-hand usually never hurts and prevents from tubes being destroyed especially when I'm dealing with client's equipment that needed be restored.

Old coupling caps usually create less of a problem if any. quick test for short is usually enough

Now about increments and waiting time. I don't think that it's necessary to wait 30min per 6V increments. If I did that, I'd have to charge client at least a grand or couple depending on unit complexity and keep unit for a month or couple. I simply slowly bring it to the point when something begins to fail or to the operational voltage AFTER REPLACING ALL DC CAPS. Voltmeters or DMM testers I connect to each tube bias pot or if self-biased to the bias resistor to measure proper voltage. From voltage as you know you can figure the current and if you can't you'll need to go via basics of electrical circuits.
Current = Voltage/Resistance

Similar methods I apply to the vintage solid state equipment. I would usually use NTE replacement transistors instead of original or NOS to run these tests. I wouldn't be worried if I fry $1 worth power transistor instead of $15 one.