Apple watch lights up periodically while charging - nightstand mode is off

Your watch is probably sensing movement and activates the screen in response. Mine is very sensitive, if it is charging on a table top even putting a coffee mug down will be noticed.

Ok, the only other external cause I can think of would be power drop while the watch is charging. You can fake this and demonstrate to see if it matches what you see, simply pull the charging cable usb plug from the powe adaptor then reconnect. If you think power drop to the charger is a possible cause I suggest you also test with a genuine Apple magnetic cable and power adaptor, make sure the magnetic puck and back of the watch are clean and aligning securely, check the adaptor is securely plugged into the wall socket (and not a dud socket), test with a different power adaptor. If the problem appears with your accessory charging station but not the original mag cable you know where to look closer for problems.