My "tack" only happens during the turning wheel phase or short after that. I don't actually feel anything in the steering column, but I do feel like the car gently bumped against something. I thought it was the front diff skipping a gear or something.

 

Some of these issues sound a lot to me like "tyre skip", some discussion about it on the Pommy forum going back several years and affecting XK, XJ, XF etc.
Put simply the front tyres sometimes "skip" on full lock, a sudden small sideways jerk felt through the steering wheel.
Only at slow speed, more often when the tyres and road surface are both cold, the road surface makes a difference, and commonly when traversing multi-story carpark twists and turns.
Something to do with the Ackerman angle of the Jag suspension design.

Edit - see here for a discussion on this a while ago on an F-Pace forum: https://www.fpaceforum.com/threads/s...nomenon.44257/