Perhaps, for confirmation, one would have series controls on opposite sides of the cockpit
With comment, yes. The comment is that you still have to allow for an incapacitated pilot, It must not be the case that either pilot cannot independently carry out the action. But, my mind goes to "confirm" switches/touch screen on both sides of the instrument panel, so the other pilot can command either a "yes, continue" or a "no, don't" while cockpit dynamics are settled. Aside from a fire, which itself can wait 5 seconds, everything else in a jetliner can wait the five to ten seconds before the
second engine gets shut down. Enough time to "discuss and agree" between two pilots.
The only time I have shut down an engine is haste was an FCU runaway on a PT-6 in the Piper Cheyenne. Was was pilot monitoring, and I did not like what I saw on the fuel flow indicator. My Captain said: "We may have to shut that one down". When he said that I placed my hand on the condition lever for that engine, identified and confirmed. I watched him gently retard the power lever, and as he did, the ITT suddenly shot toward the red line. I shut the engine down, just as it passed by ten degrees, before cooling again. We agreed that I did the right thing, and ultimately saved the engine from an overtemp. Everyone was happy with what I had done, though I accept that I didn't really follow procedure in terms of waiting confirmation from the other pilot before I shut down, we had sort of pre-briefed that - sort of...
But that was a six seat turboprop, and I was thinking to save a $100,000 inspection, while everyone agreed that the other engine was perfectly fine. An airliner is a different situation - spend the engine to save the lives!