You can tell if the firing mechanism is working without live rounds, pull trigger, "click"...
You need live rounds to validate the firing pin mechanism is functional.
Since they are your goto guys, and are trusted, perhaps you should make sure there isn't a communication issue.
I check it in as "when I pull the front trigger, and the shell fires, both barrels/shells fire. I can't do it when dry firing, so I suspect I have a worn sear in the left mech. Can you fix that please?"
But it's all good. I'll find someone else. I know most smiths specialize in a few fields, not all encompassed firearms. Can any recommend a double barrel, dual trigger shotty guy?