The power-down for the coach car you describe is typical for Lionel lighting using the capacitors they have installed in the ABS 21” cars, whereas what is shown in your video for the dome car isn’t - especially what seems to be flickering when power is shut down. I’d guess a faulty lighting board in the dome car as you get the same thing when disconnecting the other LEDs.
Last time I looked, the LED lighting boards were one of the few parts Lionel actually stocks for the 21” cars. I’ve never understood why they used capacitors that take so long to power down, which looks unrealistic to me. However, if you contact Lionel they may send you a replacement lighting board. They are not hard to install.
The only other thing I can think of is that the dome car might be sitting on a section of track that does not have full/consistent power to it, but that probably would not account for your problem.
P.S. I suppose it's possible that the dome car has a different board than the coach, as in a board similar to the ones on the first run of 21" ABS cars. These in fact have two capacitors on the board, which 'way back when they were issued Mike R. described as "super capacitors." They certainly stay lit a long time after powering off, and by the same token take a long time to power up. I think that in later runs of these cars they were changed to charge more quickly and thus reach full illumination faster/more realistically. I can't recall whether my later cars have the dual capacitor set-up; they do function better than the first run.