First there is no guarantee it goes there..
Step one: Check to insure there IS an aux coax cable.. I mean on my Video switch, from the factory, that conneciton was "N/C" (not connected).
If there is: Get ye to a store (Harbor freight) for a Cable Tracker (Assuming you do not know where the other end is) and track it.
If you do know where the other end is but... Ther eare multiple ends there....
Disconnect cable from switch, Measure resistance, center wire to nut.
Should be open cirucit If it is .. Short it
Take a paper clip (Small diamater) or if you have a bit of damaged coax a bit of center wire and your meter, Measure hole to threads
The one that is dead shorted.. Most likely canidate.
now open the short and re-measure If short now gone, you found it.
Home is where I park it!