As I see from your comments that the 604 and the 601 have the same design for the collector tank. If you know is there an associated EICAS message for low fuel in the collector tank(s)? As I know the Gulfstream 5 and 550 have such a warning. Now how would someone know which collector tank is "low"? I don't know.
I believe there may be some relevance if in fact both engines quit at the same time (some floating remarks about the possible inadvertent shutdown by one of the two pilots during the manipulation of flaps, etc) if it was in fact fuel starvation AND there was fuel remaining in the wing tanks, sufficient fuel. I did have a close friend with our local FAA (South Florida) tell me that there was a theory that in fact the control/thrust levers somehow travelled to the cutoff position. That would be significant if true obviously.