I had a jeep from the same era once (06). The tail lights are several wires; you may want to check the wires for continuity. Intermittent stuff sounds, to me, like they've rubbed against the tub and created a small open short. It's possible that they are shorting at rest, and while the vehicle is jostling around in driving (a scientific term regarding jeeps) they are freed momentarily from the short state.

It is possible that the crack has something to do with it, too, but I'd expect it to affect all light functions in that case, as it would have to be water interacting with the bulb socket for it to do anything.

Had a quick google before I crawled out of bed to get ready for work, but couldn't find much. Here's a similar sounding issue

I'd pull out a voltmeter and check what's going on at the pins for the lights.

Here's a link I found to the service manual in case that helps: https://www.dropbox.com/scl/fo/y2xpmlxsqeu6pnog3lie6/h?rlkey=213q0rnrpk3cdebmg81afa6v1&dl=0

Edit: also found this, do you have dash cluster/marker lights working? If not it might be the switch, which should be cheap to replace and a lot less annoying than tracing wires to find a short lol. see post #12 for how to check the switch https://www.wranglerforum.com/threads/no-dash-lights-or-park-lights-on-tj.2413629/