Sorry you had this happen with a new speaker. It's a real pain to have to return a defective speaker. The good news, as I see it, is that it seems to be a straight forward problem.
I'm having a hard time picturing how the switch could actually fail this way. I assume the tweeter level knob is mounted on the shaft of a discrete switch assembly. (found the picture below to back it up) Unless the switch isn't attached to the circuit board and is just rotating, I don't know. Or just an empty switch? If a multimeter checks out as suggested by Blumlein 88, and you want to listen to it while getting the issue resolved, I'd probably give it a listen, thinking that the switch is either stuck in the -0- (neutral) position or an open circuit. Take any advice from me with a large lump of salt, I had a 30 year career in switches (military and commercial aircraft ) and own a pair of F208s but I'm mostly guessing.
Anyway, it seems that getting access to it shouldn't be a problem. If it were me with this issue, I'd have already unscrewed the terminal plate to take a look, although the smart thing would be putting it in the hands of the seller. You paid good money for a working speaker!
I believe the switches are mounted to the circuit board which is visible, and can be accessed though the front panel port (if you have small hands like I do) under the damping material if you need any access from this side. I dug up this picture from the 6moons review if you haven't seen it.
Good luck with getting this resolved.
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