bluejay

See this link https://en.wikipedia.org/wiki/Cathode-ray_tube#High_voltage

What year monitors do you have?  In the 70s and maybe early 80s some TVs had a sub-power circuit that kept filaments energized for a fast warm up feature.  If you turned on the TV after it was unplugged, it would take much longer for it warm up.  Some had a sub-power switch...you'd flip it to "vacation" to conserve power while out of town.  When I was a kid, I remember looking through the vent holes in the rear of our TV and seeing the filament glow while the TV was turned off.

Do you have a kill-a-watt?  If so, plug your monitors in and see if they draw power while turned off.  It would be interesting to know if something as old as your PET monitor does that.

@Turbo-Torch The PET monitor is anywhere between 1977 and 1981(most likely after 1979) and the Apple monitor is probably around '81 to '85. 1702 is most likely between '82 and '84, and the Toshiba TV is 2001.

There's seemingly no difference in the time it takes to warm up whether I power it on while being plugged in for hours or seconds, so I think it's just the small monochrome screen that warms up fast.