How to set up a failover node/pool?

The only thing I can think of would be to build a special command handler on your servers and then when you detect you need the services restarted, modify the payload to the backend server to trigger this operation. Then on response to the BIG-IP, you could reset the original request and issue a HTTP::retry to send the original request to that secondary server.

something like this comes to mind:

when HTTP_REQUEST {
  set ORIG_REQ [HTTP::request]
  set $needs_reset (decision logic goes here)
  if { $needs_reset } {
     Change URI to special reset command on server
    HTTP::uri "/reset_services"
  }
}
when HTTP_RESPONSE {
  if { $needs_reset } {
     Revert back to original request and retry
    LB::reselect
    HTTP::retry $ORIG_REQ
  }
}

You may have to issue a HTTP::collect in the HTTP_REQUEST if you have a large request payload and then process the logic in the HTTP_REQUEST_DATA event instead.

Hopefully this gives you some food for thought.

-Joe