I have the same problem, but with a 2024 Defender 110. It looks like they changed the locking system entirely, since there is no left (when looking at the head rest from the front of the car) button at all. Nothing!
However, the following YouTube movie:
shows what may be my situation, but only mentions briefly that to dislodge the pin, you need to give it a sharp strong pull to dislodge the pin or a whack with a mullet on the head rest. Has anyone done this?