2004 trx250tm starting problem

Hello all. I have a starting problem. This is an iternitant problem. When the neutral light is on and the starter button is pushed the starter solenoid click and the neutral light and the reverse light goes out and will not come back on. The 4wheeler will start with the pull starter. After it sits or runs for a while the neutral and reverse light will work again. Hit the starter and they go back out. Battery reads 13.5 volts. Funny thing is if you jump the starter solenoid terminals you get nothing. No spark or starter motor.