New to me Barracuda with Mopar Crate 390hp low oil pressure

I changed the 11 year old Optima Red Top battery. When at low idle, hot engine and the electric fan on the volts are near 12 and slightly bounce up to 12.5. Oil PSI reads 2-5psi. But once the electric fan stops. Volt meter is back up to above 13 and oil psi is around 10-15. Gauge is not marked below 25. So I have to guess.

mechanical gauge is in the mail.

Looks like the prior owner wired the electric fan to the Painless wiring brand fuse box. I’ll change this to a relay and pull power directly from the battery.
Sure sounds like your problem is in the electrical gauge. And one other contributor to that situation would be that the alternator output voltage will drop as RPM drops low, and will also drop as the alternator gets hot. If the alternator is on the small side and not up to the job of supporting the current draw of the fan, then that will make it even worse.

And FWIW, when the oils get really hot, the synthetics will maintain as good a viscosity as a dino oil, and when reeeealy hot, like under hard endurance racing conditions, will maintain viscosity better. So a hot temp pressure issue is not gonna see change much if at all with an oil type change, just a hot viscosity change. At lower temps, then the dino oils will thicken up more as temp drops to what we typically consider low oil temps (like 100F), and so would show higher pressures then.