Good score on the Jeep TV, there.
I second Frank's idea to go with a 7 Pin Connector, and adapt 'down' to a 4 Pin type [or whatever is on your Play-Mor] for now. Down the proverbial Road, I would hook up and level your Trailer. Tow it down an empty Dirt Road at ~25 MPG and pump the Jeep Brakes fairly hard to see how the Trailer behaves. And, see 1st hand how much longer distance is req'd for stopping. Eventually, I suspect you'll want Trailer Brakes. Having gone with the 7 Pin 'Bargman' Connector up front now will make that Brakes upgrade much easier. Indeed, having your Brother run 2 or 3 extra Wires now - IF he's getting into the Jeep Side Panels, etc., anyway - will allow you to upgrade later to Trailer Braking and Trailer Battery Charging while Towing. All those 'Sticky' How To Guides are on here.
'd30gaijin' on here had a close call w/o Trailer Brakes when his 'light' CT conversion added enough stopping distance to cause him to 'see the light' re: that Trailer stopping issue. Might as well experience this effect in advance on a controlled conditions Test Drive vs. encountering a Maine Moose on the Road some night, eh?
Vehicle Electronics 'these days' often require a little potted 'Box' of Diodes in the added Harness to isolate Vehicle and Trailer Lights. Maybe; maybe not. Don't skimp on that if you find it's req'd. Folks are often disappointed when El Cheapo Trailer Wiring Harnesses fail too soon. There's good Jeep Forums on line you can join and Search n/c for Owner stories on Trailer Harness adaptations.
I had my Axles flipped, and now have much better Ground Clearance. No more snagging the rear Bath Plumbing underneath, as I and the previous Owner did. I go off-Road. Not a concern for you, but you do have to learn to look ahead to Culverts and Dips when pulling into places like Gas Stations with sloped Driveways, etc..
Assuming you have the same 30 Gallon Fresh Water Tank under the Couch, filling that adds ~250 Gallons of weight up near the Trailer Tongue. This really affects handling, and Jeep level. So, I tend to add Tank Water when I get to near my destination if possible... Also, remember the 1,500 lb. weight you cite is likely 'dry' weight w/o anything in any of the Tanks; no Propane; nada. That's generally how the Industry measures Trailer weight, good, bad or indifferent. You'll likely be towing at least 1 ton before you know it. I wrap my 2 Tool Boxes in a Throw Rug and set them just inside the Door [to prevent marring], in back of the Axle 'fulcrum'. This offsets some of the Trailer Tongue Weight if I carry Fresh Water. Trailer Tongue balancing isn't Rocket Science, so you'll learn to tweak conditions to fit your situation.
This identical Year and Model of Play-Mor linked below to CL for ~3 more weeks shows my Rig in exact condition and details. I like my $2,300- price paid a lot better, and my A/C was ~1 year old and appeared unused. Also, a 'free' 3,000 Watt unused 'Kipor' Generator was part of the deal. They're ~$1,300- or so on Amazon. Every bit as quiet as a Honda, and the Genny Tech I worked with on a lil issue thinks the World of them. Bulletproof, and capable of putting out much more current w/o strain.
'89 Play-Mor TTT On CL
Matching Tires and Wheels will be easy to find. Be sure to get the same capacity Tire for the Spare, as noted on the Tire Side as the 'Load Range', as an alphabetical letter. Mine are Load Range 'C', for example.