Temp gauge problems.

Still the first thing to do is get a jumper wire w/ alligator clips. Jump the purple sender wire to ground then turn the switch on. If the temp gauge needle races toward the 'H', turn switch off ( this zero resistance condition for extended period can damage the gauge ) and replace the sender. Temp senders do just up and die for no apparent reason. Maybe water eventually gets to where it shouldn't? I don't know.
The oil sender has a pizz poor wire terminal ( slides horizontal over a little round button contact ) and on a LA is down below behind the distributor. Its not uncommon for that terminal to get bumped off the sender. Short that gray wire to ground, light should come on with switch on if the bulb is good.