What is the most common way to configure failover triggers on two ASA running in multiple context mode?
It seems that there is any easy approach in which the standby takes over only if it loses connection with the primary on the configured "failover lan interface".
What kind of other options are there? What about configuring failover if either the trunking uplink (to WAN) or trunking downlink (to LAN) interfaces on the primary go down?
You just need to enable interface monitoring for your sub-interfaces in the context where they are allocated. The ASA will then failover if the e0/0 link goes down or if the devices can't send/receive interface monitoring packets on any of the enabled subinterfaces. For example:
firewall001# changeto context MAIN
firewall001/MAIN# conf t
firewall001/MAIN(config)# monitor-interface inside