2013 Ford f-150 transmission switches from first to third at idle

Hello, transmission concerns where there is no engagement when expected, or the wrong gear is present when another gear is expected is often due to an internal hydraulic issue. Certainly electronic transmission diagnostic testing can occur using a proper Ford diagnostic tool that can monitor electronic solenoid and component operation. However, I expect all that will be "normal" and the response from the transmission will not be. Use this link to find some shops near you that can help with your concern: www.repairpal.com/repair-shops