Non-contact voltage tester can't find cause
A non-contact tester is wholly inadequate as a stand alone test instrument. In the right and skilled hands it can be of assistance and reduce the overall trouble shoot time.  In an amateur's hands it is useless. For an amateur it can tell you if voltage is present in a lamp cord of hot side of a receptacle, very little more.  It was never designed to do more.  A genuine VOA meter is a minimum to look for faulty wiring problems. Big Box stores is a good place to get one. P.