I installed several of the Bestop carriers on old and new GW's and Cherokees at the Jeep dealership in the late 80s till 91 and something about that rack doesn't look right. It appears too wide. The width between the lower holes on the end cap should be 67 1/2" and 67" between the uppers. The Warn brand rack I saw used a pair of long vertical end brackets like the ones I see in your photo, but had a taper on the bolt hole side to match the sloping edge of the quarter panel and cap. I can't remember if there was a separate tapered bracket or if it was one piece.
The Bestop kits I put in had L-shaped steel brackets that mounted to the quarter panels and wrapped around the quarter panel end cap just above the taillights. There was also a bracket that mounted to the tailgate toward the drivers side that had a rubber bumper on it to dampen vibration I assume.
Below is a photo of the inner backing tabs inside the quarter panel.
Those tabs backed up the exterior plate on the quarter.
The shot below shows the mounting holes for the plate over the taillight.
You can see how years of vibration tore up the end cap and tailgate.
There was a hinge bracket on the passenger side that used the existing factory bumper bolt holes and was inboard of the taillight so it and the vertical tube didn't obscure the light.
Now looking at the mounting bracket on your carrier, I see a tall angle channel with much more spacing and height.
I am no expert for sure, but that looks like a carrier that was mounted on a brushguard or rear cargo rack...which may very well be an authentic Bestop made unit for an FSJ, just not like the ones I put on.
I hope this helps you out.