but I still don't understand why the monitor goes black for one second.
The monitor goes black because something is disturbing the monitor circuit. It is not affecting the PC otherwise the PC would reset, as they tend to do at the slightest opportunity.
The problem occurs when a second supply is connected. This second supply is floating with respect to the monitor and so when it is connected the ground of the power supply and the ground on the monitor are brought to the same potential. This causes a very short inrush of current which disturbs the monitor’s operation. The result is that some protection circuit in the monitor shuts it down. Then the inrush stops as the two supplies are now equalised and the monitor comes on.
Just as a test remove the LED strip and just connect the power supplies’ negitave terminal to the rest of the circuit. It should still happen.
I didn’t ask before but I am assuming the monitor is a CRT one.