We tow a 2020 Jeep Cherokee Trailhawk with no issues. Granted, Jeep has resolved this issue at the factory and needs no wiring harness.
My suggestions are like others have said.
o Check front end alignment with caster set to upper limit of recommended spec.
o Tow bar level with Hitch tighteners on all draw bar to receiver connections including drop receiver, if used. This will take a lot of slop out of the tow bar setup and make it much quietter also.
o Make sure the Jeep battery is staying fully charged while towing. We have towed without a charge line, but installed one just in case. A self contained power pack/jump starter could be used if necessary.
o If problem persists- Take to Jeep dealer to confirm towing wiring harness is working correctly.
Good luck with your Cherokee. We love ours as a toad!