I would check and make sure the wire is on the neutral light sensor, first. If it is, I would check the neutral light sensor. A repair manual should show you how to check it. If you don't have a repair manual you can download one for free at this link.
http://www3.telus.net/leneng/pdf/Honda_Trx_350_Rancher_Service_Repair_Manual.pdf
http://www3.telus.net/leneng/pdf/Honda_Trx_350_Rancher_Service_Repair_Manual.pdf