I had the same problem with my '03 and discovered the selector knob was broken, replaced it and that fixed the problem.
Yes, that should fit no problem
The 2003 Jeep Wrangler has 16 valves.
The 2003 Jeep Wrangler is a gas-powered vehicle.
The 2003 Jeep Wrangler has an inline 4 engine.
The 2003 Jeep Wrangler has a 5-speed manual.
The 2003 Jeep Wrangler has double overhead cam (DOHC).
The height of the 2003 Jeep Wrangler is 5 ft. 10.9 in. (70.9 in.).
The maximum payload of the 2003 Jeep Wrangler is 800 lbs..
The 2003 Jeep Wrangler has a 42 degrees angle of approach.
The 2003 Jeep Wrangler has a 31.9 degrees angle of departure.
The 2003 Jeep Wrangler runs on regular unleaded.
The curb weight of the 2003 Jeep Wrangler is 3235 lbs..