This is one of my pet hates…
"…one on each end." or rather, after useful comments,
"...one at each end."
Saves so much confusion.
"two combination locks on either end"
"two combination locks on both ends"
That's 4 locks you have? No, so it can't be those.
one on either end
Colloquial, but OK at a push.
one on both ends
Just clumsy. You can't have 'one on both ends' you need two, unless you can bend the laws of physics.. The one just can't reach to both ends at the same time, it needs its partner at the other end.
Further explanation as to why it ought to be 'each' not 'either' in this scenario
I have a watch chain & one watch. The watch can go on either end of the chain. No confusion, the choice is right there, either end, pick which end you attach it to.
I now have a watch chain & 2 watches. I can attach them to each end. I cannot attach them to either end, because as soon as I've attached the first one, I have no choice then but to attach the other one to the other end. I can no longer attach it to either end.
Also, the football example, of how to really fall over when getting this wrong…
"In football they have two goalkeepers, at either end…"
Sorry, no they don't. The goalkeepers don't get to choose which end they stand at, otherwise they could both choose the same end. They must stand one at each end.
BTW, I realise this is extreme pedantry, & that you could easily get away with most of the alternative suggestions, but I'm just trying to nail this one down logically