The fact the smaller working light was closer to the T, whereas the larger nonworking one was further south suggests to me, the larger one was likely in his coat pocket and perhaps slipped out during the more intense portion of the struggle.
I can't imagine GZ would have bothered with it after it wasn't working after several taps. If its dead, its dead and if banging it several times doesn't work, continuing to do so another dozen times probably won't help either.
Being that it doesn't appear to be larger flashlight, like a Maglite for example, I doubt it would have much merit as a defensive tool, so I don't really see just cause for him to do anything other than slip it back into a pocket after a few attempts to revive it.
At least thats my rationale, GZ could have very well attempted to get it working again after getting off the phone, but it seems like at that point the primary concern would be trying to be aware of your surroundings.