Fall back host - how to find out what condition is causing it to invoke

You've a few options, assuming the fallback is specified in a HTTP profile;

1) Run a packet capture (as a background process) and write it to a file; inspect it closely with Wireshark or a packet analysis tool if you've one available.

2) Create an iRule which logs data under the LB_FAILED event. See here for info on some of the data you can collect and log: https://devcentral.f5.com/wiki/iRules.LB.ashx

BTW, what do you have configured for the Pool's Action on Service Down setting?