High-availability configuration produces a status of "ONLINE (STANDBY), In Sync"

One common issue to check for...

4. Ensure that both F5 1600 units can ping each other from the high-availability VLAN

What is your Port Lockdown setting (SelfIP)? Make sure it's not 'Allow None'. Preferred configurations for HA VLAN/SelfIPs are 'Allow Default' (the safe bet regardless of BigIP version), or 'Allow Custom' which includes all the ports that HA daemons use (varies across BigIP versions)