I have this pickup producing only hum when connected (even on the cleanest setup),
same hum as when touching the jack with a finger.

Installed another HS3 today in the same guitar with no problem.

Wiring was black+white together, green+bare to ground and red to output.

Connected pickup directly to guitar jack with the same result.

Tried with a multimeter on 20K and 200K Ohms but it reads 1.

Is the pickup faulty?