Are you talking about phosphor persistence?
No, I'm talking about the total time that you see a "spot" when the power is turned off. Of course, when you turn the power off, three things turn off that affect this: the horizontal deflection, the vertical deflection, and the B++. Usually, the horizontal and vertical discharge pretty quickly, due no doubt to the low impedance of the deflection coils. But, the B++ takes a while to discharge. There are two timed events there: One is the time it takes for that to discharge, and then, when that is done, there's the time of persistence. The first can be observed by deflecting the beam, and the second can be observed only visually.
As far as how a short vertical line could be burned in the lower half of the screen, I remember the really old b/w televisions when turned off the spot would actually travel down the screen before extinguishing.
I'm guessing that's due to gravity because the ions have mass. Maybe I read that in a book somewhere because I have no clue how I came up with that one ...
Some of them did (do). Most that do that squiggle. I'm sure you know what I mean; the horizontal deflection is still barely running, and gets smaller exponentially, whilst the vertical falls. That in itself demonstrates the beam is still active, and that we're not just dealing with persistence.
On some sets, if you recall, the picture reduces to a spot, which stays in the centre, and then becomes severely unfocused before extinguishing.
As to why the beam falls in some, I have no explanation for that, you'd sure think it would migrate toward the centre. It can't be gravity, I don't think. Else the beam would fall any time you kill the vertical deflection. All those TVs with open vertical output transformers with that telltale horizontal line would have that horizontal line somewhere well below centre.
Also, turning a TV on its side would make it fall the other way!
In any case, if the beam is falling at power-off, I still wouldn't expect to see burn-in like that, due to the fact that the beam energy is greatly diminished by then. But who knows? I sure don't have a good explanation for why it's burnt like that. At least if it was a straight line, I'd say it's possible someone was monkeying round with it and killed the horizontal deflection and turned the vertical size down and off-centred it.
Hmm... I wonder if a momentarily greatly increased line voltage (line spike? lightning?) would cause the horizontal deflection to fail. That might explain it, rather remotely. But, if the horizontal oscillator stops, there shouldn't be any HV...