What type of gear oil would you recommend in the front and rear end of my 1981 Toyota 4x4 truck? Your help would be greatly appreciated

Strange cab light situation. My 1981 Toyota 4x4 cab light no longer goes on when the door is open. It does go on once the truck is started though and works properly. Once the key is turned off then it does not work again regardless if the door is open or closed. I did have a new starter put in it not to long ago. Could they have wired something wrong? It has always worked properly until pretty much around that time of the new starter. What should I check? Thanks for your help!