Thanks for the replies! I now have a theory for what's happening.
I think the processor in the Chapelon may boot a little slowly. The TIU sends the Watchdog before the Chapelon is listening. Removing the Aux Power input makes the TIU delay sending the signal by a little bit. (It now has to boot before it sends the signal.) With that little delay, the Chapelon is listening when the signal is sent.
Or maybe I'm full of bologna.
Bob