F5 Failover

I was wondering if anyone can tell me how the failover of the F5 would work or look like.

Also correct me if I am wrong anywhere.

I have three ESXi hosts,

ESXi1 BIGF501
ESXi2 BIGF502
ESXi3 Standby

To my understanding you would NOT want BIGF501 to failover (vmotion) in the event of ESXi1 failure.

Why is that? I think it has something to do with the licensing but is another reason?

If everything is setup correctly and ESXi1 were to fail and not come up in a timely fashion how would BIGF502 be promoted to the PRIMARY? Would it be similar to Availability Groups where as the SECONDARY would automatically be your PRIMARY and when the OLD PRIMARY Comes back up it is automatically your SECONDARY?