2004 trx250tm electrical problem

Hello all. I’m having a flustrating el problem. The neutral light flickers. The starter will not work. The solenoid click, but starter motor won’t engage. I can’t ever jump the solenoid and get it to work. Headlight only work sometimes. I’ve checked the battery it checks good and I’ve charged it and that made no improvements. I’ve wiggled every wire and cleaned the 2 large ground connects at the rear. What am I missing? I should add, it can be pull started and runs great. With the atv running the neutral still flickers.