We had a similar discussion with regard to manual fades, now on a major choreographed production there is no choice but to follow exactly as called but when running a play or touring a show it is a team effort to give the paying public the best product possible and in most situations I have worked in, the lighting op has the best real view of the action[not video].
I personally watch the entire show, boring or not, in case I lose a light or see a problem and if something goes wrong I will take whatever action to try and ameliorate the problem.
If the actors lose 2 pages and bring on a cue before time or if some catastrophe happens backstage I will carry on doing cues.
The "I'm only following orders" mentality may be all well and good at the Bolshoi Ballet, but on tour I'd rather have someone with a bit of initiative thank you.
In my chequered career I have been truck driver, board op, lighting designer,
stage manager and producer and have managed to make mistakes in most of them and I appreciate when someone uses a bit of common sense to salvage a situation.
Actors are not the only ones to ad-lib when things go wrong.
Briefly what some consider to be "professionalism" I consider to be rank amateurism.
Cliche as it is I believe the show should go on and everyone in the team should work together and cover each others problems.