Random issue. Jeep randomly doesn't crank over. Lights turn on, everything seems fine but no crank just the click of it engaging but not turning over to start. This happens randomly. If I get out and tap on the battery terminal posts starts right up. Other times starts with no issues what so ever. Just randomly get that click with no crank. So, possible starter issue, neutral safety switch (as it's a stick), something else? Thoughts?

(Battery, alternator and starter are all relatively new, all less than 2 yrs old)

 

Might just be loose or corroded connections.

 

You answered you own question... Clean and tighten the battery cables. While you are at it you should clean all of you grounding points.
Just because parts are less then 2yrs old doesn't mean that they can't be bad.

 

use a good battery post cleaner, and use some Ox-gard on ground terminals (NEVER use in pin connectors, etc.) and make sure the cables are properly tightened