Oil cooler will help, there are thermostats available to help prevent overcooling, mount it where it gets good airflow but not so it get pounded by rocks/road debris
My old datsun had the same problem
The flasher unit was stuffed, if skylines have a flasher unit (small metal cylinder ) that sits under the dash then I reckon thats where the problem is
If you have had a rat in the engine bay then best check all your wiring too as the furry bastards nibble on anything, I had one have a good go at eating the underbonnet noise insulater on my 300C