I don't have a Model S, but an X, but it has had the same issues.
From my experience there have been two places that I have gotten the "clunk" from:
- Sway bar link bushings
- Bad air struts
I have had both of these and unless you look on a lift, it's probably hard to tell which it is. And they both sound the same. Sometimes Tesla has to put chassis ears on the car to narrow it down but I think it's actually easier to remove the sway bar links from the equation and they can visually inspect that quickly once it is on the lift.
The other day I needed another air strut replaced. I took the technician out for a quick drive on their "bumpy test track" and we did not even get out of the parking lot before his eyes lit up and he stated he was 98% sure it was the strut, so we just turned back to the service bay. One hour later they had replaced the air strut and I was on my way with a "clunkless" car.
And yes, the mobile tech cannot do anything in this case except agree with you that your car clunks.
Also don't go to the appointment unless they guarantee that they have the strut in stock, dedicated for your car. You don't want to find out it's the strut and they have to order one.