Although PreCheck isn't guaranteed for any given flight, I would hardly call it random or unpredictable. I would say there is something amiss with a PNR if it doesn't appear on the boarding pass of a TTP while traveling on a participating carrier.

That said, one can hypothetically have a GE card and be a GE member yet be on the PreCheck Disqualification List as a result of attempting to bring certain prohibited items through the checkpoint (firearms, for example), or getting into an altercation with a crewmember. Also GE status can be revoked, but the GE card can remain in the possession of the traveler.

So just put the number in your PNR and make sure your name and DOB match (gender no longer has to).