Okay, perhaps this is a long shot, but worth checking...

Maybe the jack socket doubles up as the off-switch for the active components?

If your pickup uses a battery, the jack socket could be a 'stereo' (Tip Ring Sleeve) type, and it needs the ring and sleeve connections to be shorted to 'switch' the pickup on. Some jacks may not be doing this properly simply because of the profile of the connector.

The advice to sort through your leads for ones that work and carry a couple with you is probably wisest. Maybe carry a tuner-pedal, too - then you plug their lead into your tuner-pedal...