Glad you bring it up. Trencher's Cave has intrigued me for some time. It's one of those caves that took me several trips to find - except that I still haven't found it yet!
I have made 2 concerted efforts together with domsmooth on different trips to find it, with no luck. We have narrowed it down now, and I'm pretty sure we'll get it the next time we try.
We have explored the Northern face of Cathedral Peak pretty thoroughly, approaching from the neck at The Bell, as well as from the base of the cliffs approaching via Bugger Gully. On the 2nd attempt I had calculated the waypoint from the hiking maps and punched it into my GPS. It took me to the edge of a small rock band below the strip of steep, grassy slopes directly under the towering cliffs of the North Face. No luck. Did find a small 2-man cave in the face though, kind of a mini Roland's Cave. It was full of Dassie droppings, and required a precarious climb to get to it.
What I would do on the next attempt is to approach via Bugger Gully, get as far North as possible (Right, if you are looking at the peak from there) and scramble up towards the summit, looking for hidden grassy ledges, where I suspect it lies. This is actually what is suggested by the map, but somehow it's not that obvious when you are actually out there. If it's not there then it lies much lower down than indicated on the map.
So far the only people I have spoken to that have been there were the local rangers. They described it as a basic overhang.
Good luck, and if you manage to find it, please take pictures and let us know!