From an insurance perspective, what would happen if I left the a/c and it 'did its own thing'?
Good question TC. If I may add a few more questions to your posting that may be worthy of further consideration.
What would happen to the pilot's licence?
What would happen in the event of injury/damage to third party? Would the insurance, company or personal, cover said pilot against claims? I doubt it very much.
I think I will continue to do what I have always done, shut down and investigate, much better option.
Fly Safely,
Chopperman.