I just came on to post asking for help with probably the same issue. I have attached a video with that demonstrates my issue.
I just had Tesla mobile to my house and the technician told be to bring it in. I imagine they were "hoping" for the loose steering rack issue.
The technician drove the car with me and thought it was a steering related issue, as I did too. But he concluded it is likely a front suspension issue, more specifically the upper control arm ball joint. The upper control arm is non-serviceable, the ball joint is riveted to the control arm and is not grease-able, on my 2014 S with coils anyway.
Replacing the upper control arm seems pretty straightforward, but I am having trouble diagnosing if that is the real problem.
I jacked up the car, driver's side, and tried to 12 and 6 test, holding the wheel at 12 and 6 o'clock and basically heaving it, looking for play in the wheel, but sensed none, same for 9 and 3 o'clock. I pried up on the tire from underneath, seeing if the upper control arm ball-joint had vertical play...but there was none. All the boots/seals look good on the ball joints. I can tell that both steering links, where they attach to the knuckle, had grease coming out at some point, as they are slightly stained, but seem dry now.
Any thoughts or advice would be great. I'd really like to tackle this myself if possible. Thanks
IMG_0849.MOV