From the 2002 appeal.
44. Daniel had received five wounds from a gun to the back of his head, which appeared to have been fired in an arc and in quick succession. Nicholas had three gunshot wounds to his head.
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There does not seem to be much on them. Which is not surprising. Unlike Neville, June and Sheila, they were shot, killed and found in bed, while asleep.
The twins being asleep supports the assumption that Sheila slept through the massacre until it was her turn. Just as the twins did.
The statement saying Daniel's shots were fired in quick succession also suggests both of them were shot multiple times in one visit. Rather than shot once each before being shot again later, as posters have suggested.
The twins being shot in their sleep also incriminates Bamber. As surely the twins would wake if Sheila was having such a serious long term psychotic attack that Neville had to ring Bamber and the police. If they didn't wake, Neville would wake June and tell her to go to the twins.
Bamber would try to kill the biggest threats first, Neville and June. Who were next to each other. Shooting the twins first risked Neville and June waking. Bamber being up against two awake, fully fit and out of bed adults would put his plan in serious trouble.
It is not clear whether he shot the twins or Sheila first, after killing June and Neville. Shooting the asleep twins first would mean no noise which would wake Sheila. He then had time to do what he needed to do with her.