Why does my iPhone 12 pro turn on & off during the night while on the charger?

Any number of things could make your phone turn on during the night. You could get a notification, such as an email, a text or an application like Facebook, Twitter, etc. The phone may stop charging during the night if Optimized Charging is on and it could ding when it picks up charging during the night.

To avoid having your phone notify you of anything when it's charging and you're asleep, put the phone on Do Not Disturb. Mine is set on DND from 11:00 PM to 7:30 AM

See this link about how to set up DND --> Use Do Not Disturb on your iPhone, iPad, and iPod touch - Apple Support

Is it just that the screen will light and go out? If it is just the screen lighting up and going off, it would seem there is a power issue for the power adapter and charging cable. It could be disconnecting and then reconnecting again. If the iPhone is turning off on its own, then something isn't right. You would need to be able to determine which it is that is happening to be able to troubleshoot further.

Your phone will turn on briefly any time it receives a content update or a notification. This is normal. If you don’t want to be alerted turn on Do Not Disturb manually, or set a DND schedule.