When I worked in the UK for a well known charter company flying twin jets we were told that unless you knew the reason the engine had failed then leave it alone, (shut down), divert and land on one.
If an engine stops there has to be a reason and by re starting it you may just exacerbate a condition and finish up wrecking the engine, such engine damage is not covered by the normal hull insurance and the cost of a new engine falls on the operator.
Obviously if it is a matter of life or death then, as in Capt Moody's situation, relighting would take priority.
Just another viewpoint for consideration.