I have a 2011 jeep wrangler with 46,000 mi. I bought a 2014 5x8 trailer. The parking light fuse on the drivers side blows when I plug the trailer in.

 

Welcome to the forums.

What size fuse is that ?
You need to determine if the fuse is blowing because it can't handle the additional load or is there a short in the wiring.

 

it's a 15a fuse. Is there another fuse I should put in for a trailer?

 

NO! Do not put in a larger rated fuse. Check your trailer. How many lights does it have. What you have is a larger than rated draw on the car system. Now this might not be your problem but its worth investigating.

We had a similar problem with a 2010 Jayco popup. My son-in-law's KIA Sedona would blow brake light fuses continuously (however,my GMC Safari and my son's Blazer did not. So we did not attribute the popup as being at fault.). After much expense and checking with both Jayco and Nissan it was determined Jayco had too many lights being used. They have since reduced the number of outside body lights. My son-in-law solved the problem by going to the expense by installing quality LED lamps in all brake and side marker lights.

 

How are you connecting the trailer wires to the Jeep?

 

I'm using the 4 prong plug that came with the trailer. 3 males 1 female.

 

The trailer only has 2 side marker and tail lights. Would it do any good to pull the side marker bulbs?

 

I would start with the trailer by itself, remove the bulbs from the trailer, and visually inspect each socket for any sign of corrosion, etc. With the the bulbs still out of the sockets, and using an ohmmeter or continuity tester, you should have good continuity between the female connector and the frame of the trailer, and you should not have continuity between the female connector and any of the three male connectors. If you do have continuity on any of those three wires, that wire is shorted someplace. Not guaranteed to reveal the problem, but that is where I would start.

 

You definitely have a short. A 15A fuse is plenty to run those lights.

 

I noticed the tail light bolts were loose. Does that have anything to do with the ground?

 

Loose bolts will definitely cause the bulbs to flicker without a solid ground but they shouldn't cause a fuse to blow.