Another scenario that the facts seem to fit.
Mainly as I was surprised by the John Farley comment earlier in this thread, I thought I'd point out the obvious bit that nobody seems to want to consider.
If, and I say again IF, Sgt Nightingale had lifted the weapon from another combatant and tucked it under his pillow, intending to keep it for his post army career as a hired gunman back in the UK, things would not look much different.
That would certainly explain why he didn't hand it in at the armoury on return from patrol like he should have. Regardless of how he got it, there are procedures in place for coming back in to camp with a gun more than he left with.
Exactly which box it came back to the UK in can't be proved.
Anyway.....
He comes home, has the gun, starts collecting ammo and gets called away from the house where he thinks it will be safe because "we all have them" and nobody's gonna search the house.
Suddenly it's all come apart at the seams and he needs a story. The truth is out of the question, so let's fall back on the "when I was ill a while ago" story. This near death experience which so affected his memory and yet cleared up a treat... yeah, reminds me of a Monty Python sketch.
"He nailed my head to the floor, but I got better."
On one hand, he was so ill that he can't recall having the Glock, on the other hand, he's fine now.
Mostly I'm inclined to give a lot of weight to the fact that he decided to plead guilty and therefore avoids having to answer questions in the dock. Now that really is a smart piece of legal advice.
Basically, forget the Brain injury, forget the sudden return to the UK with the deceased. Forget the house moves and boxes in storage.
Just explain why he didn't hand it in on returning to camp the day he got it.