Usually shorts through the oil pressure sending unit... unplug that first and see what happens, then if no luck check the relay.
If it's the sending unit, just replace it with a new one. Look up how to modify your car to accept the 1988 version of the sending unit, its simple to do. They are much more reliable and a lot less expensive.
Edit: Here is the link to the modification if you choose to do it!
Red 1988 GT under restoration!
( ͡° ͜ʖ ͡°)
[This message has been edited by Shho13 (edited 03-17-2015).]