So even though the JL Wrangler has the rear 12V plug, the gauge of wire it uses is pathetic and not sufficient for a 12V Fridge. Yes it will power it, but from what I hear you will lose a lot of amps and voltage from your battery. Engel recommends power the fridge to a 12V plug that is directly connected to the Battery. You can see what I did for this on my BLOG as well as a review on my Engel MT45 Fridge https://www.myjlproject.com/blog/engel-mt45-platinum-review/. This thing is NICE!!!
A few pics of the Install:
