This time I believe I got it and that problem is solved.
The first step was to realize that load balancing was creating problems. So I took care of that by excluding the target address from load balancing. But even so, the tunnel kept flip-flopping between the two outgoing interfaces.
I eventually realized that it would continue doing so as long as there was more than one default route. So I removed the default route from the unneeded interface.
set interfaces ethernet eth1 dhcp-options default-route no-update
commit
That route did not immediately disappear because the tunnel was attached to it at the time of the commit. But once I forced the switch to the right interface, it did.
To test the results, I simply did what I had been doing. Physically unplug the right cables as needed. So I unplugged my pppoe cable for about 10 seconds, and plugged it back. The router got a new IPv4 redressed and reset the tunnel as expected.
Problem solved. :-)
Thanks for the help. I could not have done it without you.