Proper toner/probe use to track coax behind drywall
The point of coax cable is to protect a weak signal from outside noise. That also protects the outside from a signal on the coax.

What you need is something that puts out a signal that can be picked up when connected only to the shield, so there isn't a balancing counter-current on the interior conductor.

I am fairly sure such exist; I can't recommend any specific products.