electrical problem

I have this problem it just happened yesterday after driving. what happens is when i shut the car off like totally off like all power off, the oil pressure light comes on and sometimes it doesnt come on right away but like a while later and it ended up draining my battery over time. also the needle on the temp gauge takes a while to come down. any help on where to look would be appreciated.

damn its abitch to trace the wire, i started today there is some kinda of short for sure but i didnt have enough time so i just pulled out the bulb, im gonna fix it on the weekend ill let you guys know what happened.

on a sr20det does the oil pressure switch send a signal to the ecu or is it just wired direct to the light in the cluster. for some odd reason that wire is always powered even with the car shut off.