If the jeep isn't in Park or Neutral, turning the ignition to Start won't do anything. It's made that way so you can't accidentally Start in gear. On occasion, I need to jiggle the gear selector (when in Park) to get it to turn over.

What's that switch/sensor really called? Is it the "neutral safety switch"?
Where is it? Could that be the problem?

 

It's called the neutral safety switch. It depends on your year jeep where it is. What have you got?

 

'97 GC Laredo 4.0
Guessing its on the side of the tranny? Hoping its a simple unbolt and swap with new.

 

You've got the 42re transmission and the switch screws into the side of the case with a plug on it. It's a plunger switch that rides on the shift quadrant inside. It also operates the reverse lights. If the jeep is still starting, it might just be a shift linkage adjustment. Does it start in neutral?

 

Yes...and 95% of the time in Park. If it doesn't in Park I just jiggle the shifter and then it starts.

 

Try just pushing it forward instead of juggling it. If it starts every time doing that, the adjustment just needs a little tweaking, not replacing the switch. I'd hate to have you replace the switch and still have the same problem. But, it's your jeep and your choice.

 

I'm guessing that's something I'll see if I take the console out? I had to do that once to fix the parking brake switch.

 

IDK never having done it myself, but if there is no adjustment at the shift lever under the console plate, you may have to bend the cable mounting anchor bracket just a tiny bit.