87 trx 350 oil cooler fan trouble

Hello everyone! I’ve really tried finding an answer in the existing threads with no luck. My problem is my fan comes on often exactly as I switch my headlight on! Sometimes it turns on with the lights off when its supposed to but I’ve noticed its not coming on when it should( ive had it long enough to know when it should)at which point I then turn on the headlight and it turns right on! And it will run a full cycle when its actually hot. If its not hot and the fan turns on with the headlight it’ll go out rather quickly. Do I have a bad ground??? Also My oil light has been acting up too. Not turning on always when I turn the key on and sometimes it just flickers when I’m riding. I don’t want to hard wire it as I want to keep it original. Thanks so much for any help!