You are not going to harm a 12AU7 preamp by hot-switching it.
You will kill a 50,000 Watt radio transmiter if you don't bring the filament up to temp before you apply HV.
The difference is: up past 300V, we can use rich oxide cathodes that have way more emission than we will ever need. They soft-limit emission, so they are very hard to harm when half-hot. And they have deep reserves of Thorium which will come to the surface as fast as it is ripped off.
Now up over 1,000V, electrons that hit the plate knock out secondary electrons and even positive ions that can hit the cathode pretty hard. So we have to use different cathode materials to withstand bombardment. But these thin tough coats can be stripped to the bone in seconds.
"Home radios", including most tube audio applications, just do not have to worry about pre-warming tubes.
Thermal delay relays are as old as tubes. They are essential on Mercury rectifiers, which can behave very badly if not heated before HV comes on. A thermal relay often looks just like a tube, on octal or 9-pin base, but inside is a heater and a bi-metal contact. Usually you just give a fixed delay, it isn't real practical to measure cathode temp and if a tube is happy, its warm-up time is pretty consistent (especially since series-string TVs appeared).
Of all the audio I've worked on (ignoring radio transmitter gear), only one had a delay relay. The biggest Dynaco tube amp has one. I can picture two reasons: a concertina driver can cause a full-power THUMP at start-up, and with this 120+W amp in a world of 40W reflex speakers, maybe it was a problem. Also the 8417 output tube is very high-strung, Dyna ran them at quite high G2 voltage, and maybe they gave trouble and maybe Hafler thought a delay would be better (actually, I think the 8417 is just TOO high-strung). But I've run other quad-8417 amps without no silly delay-relay without problem.
Fender amps are a special case. Fender raised B+ far above the ratings. In gig work, power/pound is more important than thousand-hour life; also Fender did consult with tube makers to push the limits without begging for problems. And many times, the amp buzzes too much to leave it on through breaks, yet you might get called back from break and forced to play instantly. The Standby switch kills the buzz and lengthens the life of these abused tubes while allowing instant pick-up.
If you still want a pre-heat: just give 10-15 seconds delay. That's twice as long as any common tube needs.
If you gotta be clever: put a 10mA relay in series with one section of an extra 12AU7 wired to an instant-on voltage source. You will have to tinker to get things to work right.
