Re: the previous statement having to do with telephone cables.
Shorts to ground or to another wire in the cable was located with Loop and Varley measurements with a Wheatstone bridge. Opens are another matter.
Thinking WAY BACK, when I first started with the phone company and cable and open wire was still in use, there was an insturment for locating opens. It was an ancient piece of gear even then.
But I digress. The machine used a capacitance "kick" as the capacitance of the wire was charged and discharged and a capacitance bridge to detect the distance to the open. Battery and ground was alternatly switched off and on the open wire and the bridge was balanced via a Leeds Northrup capacitor box for a minimum kick on the galvanometer. Since the capacitance of the cable pairs was known, it was easy to calculate the distance to the open. The relays clicked about once a second or a bit slower.
Bear in mind that the capacitance fault location was not nearly as precise as a resistance type of fault. And the locations for either were only as good as the initial cable installation measurements.
I just posted this so you will not spend time looking at what the telephone co. used, since I don't think that this method will help you to locate an open in a coil of wire.
There are distributed capacitances between turns and layers in a coil, so you might come up with something anyway.
Good Luck.