Electrical fault tracing
Both a non contact tester and a voltmeter will show voltage on a disconnected wire that is running parallel to a hot wire. Using A load like a light bulb put on the red wire to neutral will take the voltage closer to 0. If there truly is a short from another hot wire to the red the bulb will light. If the bulb lights the short could be in any junction box or at a staple holding the wire in place, the last possibility is a nail or screw was driven through the cable. There is a tool that can scan through walls that some electricians have that can pinpoint an open or short through the walls. I would double check and verify the voltage with a load because most times it is just induced voltage from running with another wire.