What happens when the active member of a LTM VE pair reaches its demo license expiration?

Mayur, I'm familiar with all of that. Those don't answer my specific questions.

It appears my expiring LTM VE instance finally deactivated itself at midnight local time, which was strange, as it might have allowed me to squeeze more time out of it if I'd just set the system's timezone to UTC-1100. It also failed over properly. This is something I couldn't find in any documentation: HA/failover behavior in an HA pair during a license expiration event.