Thanks for your question, Gregory. This is important for the gamma-ray lines you mentioned, and also for detecting possible effects due to quantum gravity. I'd be happy to go into the details, if you're interested in how we do this.
All instruments have some dead time.
This is important for detecting evaporating black holes, which may end their existence in a bright flash of gamma rays, and other phenomena such as gamma-ray bursts. That's a long answer. I recently heard of a model for GRB's that describes a supernova remnant spinning so rapidly that the centrifugal foce keeps it from collapsing into a black hole until the magnetic fields slow it down, only to learn that this idea has already been rejected. Steve, I'm not familiar with this particular model, so I can't explain why it has been rejected. The fact is, we don't yet know what causes gamma ray bursts.