Will an honest mechanic disable the customers drive camera because they don't want to be watched? One that has inside and outside views, or will he/she not care at all?
If you have to ask this about your mechanic, perhaps it’s time to look for a new one.
If he's not a shady mechanic who stands by his work, it should never need disabling.
I'm pretty sure you need the owner's permission before you can legally film on somebody's private property (his shop).
If the mechanic is concerned about any unauthorized recordings then they should discuss it with you. But no, a honest mechanic shouldn't be disabling any equipment without your knowledge or permission.
Is there some reason you don't want to just put some tape over the lens? That's what I do with my laptop camera when I'm not deliberately using it.
Not care
I wouldn't mind if my mechanic unplugged my dashcam (inside outside) when he works on my car. Not everyone likes being filmed lol. As long as the job is well done, I don't care.