For some reason nobody read all the post, if an umpire had made a dead ball declaration , in the case under study or any with plays still going on in the field it should be a dead ball mechanic. My original call was nothing of the sort. Just to correct the ones who don't read ALL inserted opinions.
The only mention I see of a dead ball was when Bretman thought the runner was continuing to run after being thrown out. He also said he had interference which is a dead ball. You asked for clarification, they clarified the OP said there was a runner on first, then you said you would signal a DDB to warn the other team the runner on second left early. Even if someone mentioned a Dead Ball, it's just that a dead ball. That's not in any way, shape, or form the same thing as a DDB that allows the play to continue. If someone said Dead Ball in their scenario, explain how you had a DDB instead? A dead ball is exactly that the ball is dead, the play is dead. What scenario would someone declare a dead ball and you signal a DDB and allow the play to continue anyway?
I'm pretty stubborn too, but if NCASA, Irish and Bret all read your post and said they read it the same way and you were wrong, you were wrong. That's like 60+ years of umpiring, a good amount of that at high level ball. I challenge you to show me where any reference says to signal DDB when it's supposed to be a dead ball, or where it says to signal a DDB when a runner leaves the base early.