I am remodeling a hall bathroom. The new vanity lights need to be moved over about 2 inches from the original placement. The old vanity lights were secured to a wall stud. The new vanity lights will not have a stud in which to secure to. Can vanity lights be installed without a wall stud?

You will need to mount an electrical box in wall, if it is a long vanity light, toggle bolts work fine. Don't go light on mounting. It also doesn't have to support an engine.