Caucasoan Blackplate, that was my initial thought, but wouldn't that make the impedance on the switch solder tabs stay the same no matter what position the switch was in? As it is, altering the switch position appears to break the circuit from an impedance perspective, but is not preventing power flowing to the circuit.
It does sound like a switch issue, doesn't it? The measurements are confusing me and I don't know enough to troubleshoot in further depth.
Perhaps it's just time for a new switch as the next step.