After my fancy Ab/Bb trill mechanism was completed, a number of interesting options have come up. The most recent, when seeking to remember the famously impossible A4-B4 trill in the last movement of Berlioz’s Symphonie Fantastique, I discovered a new one that anyone with an Ab/Bb trill key can do, and I can do easier since my thumb can just use the Bb key.
It’s kind of a down tril. Start on A normal fingering, then go to this full fingering (red trill keys down) for B, and trill open the two tone holes to go down to A. A bit fussy, and the A is sharp, but it works well enough for Berlioz and easier to get to than the other fingering I learned years ago.