Multi-engine procedure
I don't know if it's applicable to jets but in our multi-engine assymetric drills, we power up the remaining live engine as soon as the other quits and we try to verify and confirm and by that, this should've given them a clear indication which engine was in trouble. Throttling up the problematic left engine (and throttling back the right) would've made more noise and that should've given it away.
Just my 2 cents worth. It's probably easier said than done but I would've done it that way.