[Fatmanstratman]

You didn't say what sort of Tele you have.

If, as the maestro says, your neck pup is pickguard mounted, that could be the cause of the trouble. But I'm not sure that you necessarily need to body mount it.

My personal pup mounting choice is the good old fashioned rubber tube - when it compresses it acts like a shock absorber and cuts out any potential rattles. I'm not a big fan of the spring mountings, and generally discard them in favour of the rubber tubes as soon as I'm doing my first major setup.

For the few pennies involved, it might be worth giving that a go in the first instance. Also, how old is your Tele? Is it possible that a previous owner has at some time taken off the chrome plated pup cover for whatever reason and not clipped it back on firmly?