PA-31 Flight Instructor reported the right engine pressure began to drop during training. The instructor decided to secure the engine; but erroneously shut down the left engine. Reporter requested assistance from ATC and was eventually able to re-start the left engine and executed a single engine landing.

Narrative

I was in the left seat and the student was in the right seat and the pilot flying (PF). We were in contact with approach coordinating a clearance for maneuvering to conduct our training when we noticed that manifold pressure was dropping on the right engine. A scan of engine instruments revealed low oil pressure and high oil temperature. I began to secure the right engine IAW the low oil pressure checklist and the engine securing procedure.When a successful feather was accomplished; and I moved the mixture to idle-cutoff we both realized that I had erroneously shut down the left engine. I attempted an immediate restart IAW the engine airstart checklist. This start attempt was unsuccessful. The right engine was running smoothly but speed was approaching Vyse. I immediately confessed this situation to ATC; [requested priority handling]; and obtained a clearance for a descent and direct ZZZ. I re-secured the left engine to prevent engine flooding and decrease drag.As we began our descent and turn direct ZZZ; TIS-B did not indicate traffic in our intended flight path. During the descent I briefed the PF on the plan; and we developed the following shared mental model: Plan A was to safely exit the base of the clouds; quickly assess any potential obstructions and select the best forced landing area. Once that plan was successfully in place; a second air start could be attempted. I communicated this plan to ATC.When we broke out of the clouds; we implemented that plan to a successful air start. We began a climb; obtained an updated clearance; and secured the right engine. During localizer intercept I transferred aircraft control to myself and conducted a single engine ILS and landing in ZZZ.When an instructor pilot with as much experience as I shuts down the wrong engine; the obvious question is why? The reality is that no pilot regardless of experience is immune to error. I have been providing extensive training over the last two months in both cockpit procedures trainers (CPT's) and actual aircraft. In both of these situations; I am the one who chooses which engine gets shut down; it is only a simulation; and it scarcely matters which one I choose.This is not a safe mindset to have since it is possible to negatively transfer it to an actual emergency. From now on; when giving simulated emergencies; I will use the following procedure. While looking at the engine instruments (rather than the throttles); choose which one I want to simulate failure on; then use the same verification procedure on engine controls that I would use in an actual emergency. This way I am maintaining a habit pattern that will transfer positively to actual engine emergencies.