Welcome to the JOF.
Does the light get brighter when you switch it to the 'on' position? It may be that a circuit has a bad ground and is going through the bulb on the jack.
IIRC, someone posted about the same problem recently. Maybe that person will respond soon.
Edit: A number of people responded while I was typing!
Sherm & Terry w/rescues Steve (std Poodle) & Eydie (min Schnauzer)
2015 Jay Flight 27RLS (Camped: 102 nights 2015, 90 nights 2016)
2006 Ford F350 6.0 PSD, Lariat, 4WD, CC, LB, SRW, auto., Camper pkg.