Should headphones be plugged in when tube headphone amp is on?

Good question. I always have my headphones plugged in when my tubed headphone amp is on. It is a just in case practice, almost like a superstition. It probably doesn’t mater… maybe someone did the research, I never have.

Not sure what the correct answer is but there are many tube amps that have the headphone circuit running all the time and users do not have the headphones plugged in. The headphone section is not using the power amp section, or has added resistors to cut power from what I understand.

i would assume that it is the same as with tube speaker's amps - it has to be connected to load.  Open output in tube amps can result in damage to output transformer (overvoltage).