Sounds like a bad ground to the fan motor, which runs OK with the lights off. But with lights on the load is 'just great enough' to cause the fan speed (rpm) to drop.
I could actually HEAR the difference in my fan speed when I got the ground AND the primary connections better. Until then, I never knew the fan could go that fast! Fans draw a LOT of amps, which is not reflected as much by the VOLTAGE drop. If the AMPS fall off the fan slows down.
I suspect the
oil press drop is a 'red herring'. At any rate, focus on engine water temp.