Curious to know your test results.
We also tow a Jeep Cherokee and have had that problem 3 times normally at lower speeds and normally some event disturbs the motion of the Jeep. One time was a pothole another was a curb.
Bet you'll find that was your problem.
Jeep has a "fix" and it is listed in your owners manual. But in my opinion; it has not solved the issue.
2017 Entegra Cornerstone 45B with Retrobands on the front
2017 Jeep Cherokee Trailhawk Totaled
2019 Ford F150 (Thanks Tadd)
"If you ain't the lead dog, the view never changes".