Oh it's always nice when something new comes up
I've superimposed the two images in Photoshop, and you can see the slight change in perspective between the ones where it's present and the one where it isn't:
You can see the engine bell in the background, so it must be between the ladder leg and the bell. I think this is a likely candidate:
I think this shows roughly when the photo was being taken, and you can see Neil is at the LM - it'roughly at the time the only clear photo of him on the surface was taken, and he is in shot (at least partially) in other images around the time the plaque photos were taken, so it could easily be that he is moving something around:
At one point in the sequence (01:13:55 in here
you see Neil discard something from where he's working and it ends up on the floor.
The object I've picked out is missing from an earlier photo
and doesn't appear to be hanging there in a later photo:
So it appears while Neil is doing whatever he's doing, discarding something, then isn't there. What actually is it? No idea!