2011 hyundai santa fe, reverse lights staying on as long as the ignition is on. Pushing down on fuse box provides temporary fix. Any idea?

The back up light switch may be stuck on.

Have no idea of any correlation between pressing down on the fuse box and the lights going off, unless something came loose inside it. As other poster said, probably a bad switch.

Pushing on the fuse box probably temporarily cuts the power off.

I suppose that is a possibility, but again that shouldn't happen. That would indicate a faulty connection of some kind in that fuse panel, because most of the fuses should be hot at all times when the key is on for some things and other only get hot (like certain Lighting fuses) when the switches are activated), while others are hot all the time. Is there any relays in the box you are talking about? If so, see what they are marked for. It could be a sticking relay that is over heating and disengages when you press down on the lid.