AR
now that I see wher you were coming from - the do I/do I not relight the engine angle. I would go with the Wings outlined mental checklist.
Have personally experienced 2 engines out on an A330 during a test flight - #1 was a turbine overheat (cooling air overheat) indication, in simulated single eng climb, with #2 at idle. Then when we shut down the #1 (per the FCOM) and advanced the throttle on #2 - BANG - the engine surged and ran down to sub idle, it had flamed out.
As the riding engineer on the test flight, and an engine wallah. The 2 ex-Empire Test Pilots in the left and right hand seat turned round and asked "Which enigne do you think we should relight?", as they asked this question there was a thud and whirr as the RAT dropped out to give hyd pressure, this does tend to focus the mind somewhat!
We decided to relight the #1, as we only needed low thrust to return to HKG, and the overheat indication only came at CLB thrust. We obviously made it back safe.
When we got back on the ground we found that the #2 surge had only been an airflow issue, no physical damage had occured in the compressor, but because the enigne had rundown to sub-idle, in-flight - do I/don't I relight it logic suggested it could be damaged. But, it's all about what you observe/feel at the time.
I hope this is a good example for you.
Safe Flying,
N1 Vibes