The problem with that approach is that it can be attacked as arbitrary and capricious, and/or discriminatory. "The inspector didn't wear a body cam when he inspected their new deck, why did he wear one when he inspected mine?"
We're pretty much certain that if the department is going to use them at all, use will need to be based on an established policy. Either turn it on when you arrive at your first inspection and leave it on until you leave your last inspection, or turn it on when you arrive at each inspection and turn it off after you're back in the car and ready to leave each inspection.
What we're less certain about is whether or not to use them at all.