[07lmnt]

The red wire is the ground side. The voltage regulator is supplying a variable ground dependent on dimmer position. I would cut the red wire near the cluster and using a 12v incandescent test light connected to battery+ it should light and dim. If not the cluster is the problem.

Cold solder joints are a known cluster problem.

 

[07lmnt]

Experience has me not trusting those power probes thingys. Lead you right down the rabbit hole.
A 12v test light still has it's place in modern cars, it will load the circuit slightly. A DVOM will not load a circuit and can fool you into false results too.
10-12mv on the ground side is a small amount of voltage drop in the circuit, should not be enough to make the lites inop.
When it acts up again , ground the red wire. If the lites work, it's a problem in the cluster.