Welcome to the pita world of electrical debugging
Ac vs dc - ac current flow makes electric/magnetic fields that induce voltage/current in nearby wires - a non-contact sensor is a "wire" exposed to said field and wire is connected to a regular high impedance multimter like circuit. It's the changing that makes it pick-up-able.
A normal voltmeter reads voltage via contact. Impedance is how much current gets tapped out by the contact. Small current/high impedance disturbs what you're measuring the least. But with testing trailer wiring you need the wiring to be able to hold it 12v voltage when the lower impedance light bulb sucks its load current. Or else the bulb might not light up.
One method of tracing power down a wire is to poke the sharp needle end of a test light through the wires insulation working from the last known good location outwards towards the load. If power gets to the bulb and it still doesn't light up that's when you provide a know-good ground to prove out if the existing ground has poor continuity ie extra resistance preventing good current flow.
I'm a believer in running explicit ground wires and not relying on a rusty corroded frame to be ground. If a light barely works you can measure dc voltage at the bulb ground pin - if its a volt or 3, there's undesired resistance in the ground path, most likely corrosion. If its basicly 12v then the ground path is an open circuit.(broken)
Solder all connections, don't use those little insulation slicing clips , twisting wires together or marettes.