This probably has something to do with how the chassis is grounded to the AC line. I strongly disagree with grounding the chassis to a third ground wire (three wire cord), especially when the tracer is used with AC/DC sets, but you can try this anyway. If used on AC/DC sets, though, you risk blowing fuses. Try sending both sides of the AC line to the chassis through .05 MFD condensers, or just one, and then try reversing the line cord. Try shielding tubes, especially if they have anything to do with an audio injection circuit (allowing you to inject an external audio signal). Check to see how the filament transformer winding is connected to the chassis. Does it use a center tap? If not, is one side grounded to the chassis? If it is not, you may try balancing both sides to the chassis through two 47 ohm resistors, one per side, or through two .05 MFD condensers, one per side.
Experiment. If this tracer uses a shielded probe, how well is the shielding connected to the chassis? What is it connected to? What was it originally supposed to be connected to?
Shielding the tubes will likely help a lot. Putting shielding springs around leads that run above the chassis can also help if conditions are extreme. The coil springs must be suspended in such a way that they will not slide down the wire and touch such things as perhaps a grid cap at the end of the wire. Crimping the spring so that it grabs the wire insulation can help, or wrapping it with friction tap at the end can help (hardware store). One end of the coil spring must be connected to the chassis.
Start with the easiest and get more complicated only if necessary.
Thomas