I successfully updated the firmware in my main panel to 1.12 (everything works fine, including the Schlage lock which prompted the update).
I then updated the TS1 to 1.10. This was a little less straightforward – after the update, the TS1 seemed to lock, so I reset it by pressing both front buttons. This triggered a reset/reboot, and it now seems to be working fine, with the updated firmware indicated.
However, the TS1 is no longer paired with the main panel. I attempted to relearn it several times, including disabling, saving, and re-enabling the TS1 in the main panel. No dice.