I read that the best backup battery for a headlamp is one carried in a backup LED headlamp. (after all, they are very lightweight these days)
My partner could have used that advice on Orizaba once - all that fumbling around with a dead lamp, spare lamp, or bad connection, or whatever. He never could get it to work again and could have come to grief had not dawn crept around. Even on Whitney with a trail, it's nice to have 100% backup and, importantly, an easy turnkey method of making it work. Harvey