I had the same issue. I called liftmaster and they told me Tesla would only integrate with garage doors, but not the gate operators. Hopefully Tesla will give us an update for the gate operators. I also wish the CT came with home link. My wife’s Model X has home link and it controls both...
Thanks for letting us know
You may also consider Vibra-Tite VC-3 which will not loosen under vibration.
https://www.vibra-tite.com/threadlockers/plastic-compatible/vibra-tite-vc-3-threadmate/