Hm, if there is an event that tells us that the dungeon finder finished and the popup shows where you need to press "YES":
The game does an reloadui and writes a variable to the savedvars.
An external tool checks this savedvars every 3 seconds for the variable and if it finds it sends an email.
Only problem:
If the reloadui takes place the popup will most probably be gone and you are again in the queue
P.S.
I doubt there is such an event so double No for your request.
And the hint: Write in the offiicial ESO forums and tell the devs that the dungeon finder is not the way you like it to work, so they officially "fix" it.