I didn't get to try an Amiga growing up. What do you mean when saying "drag down from the top of the screen to show the high res display"?
Here is a demo: https://youtu.be/H86miOXXS48?t=534
For instance, if you have an interlaced mode showing under a non-interlaced mode, then the entire screen displays at ~480i (to use modern terms) with the non-interlaced portion doubling its scanlines. But if the interlaced screen gets covered up, then it snaps to ~240p non-scandoubled.
The biggest modern problem with this is that displays turn themselves off to resync on mode changes, which always annoyed me greatly.