When siblings share a room, the instinct is to give each of them their own everything, including a clock. In practice a second clock in a small shared bedroom creates more arguments than it settles: two displays glowing, two sets of buttons to fiddle with, and two alarms in a room where one child needs another half hour. One clock, well placed and agreed on, works better.
The thing children actually argue about is not what time it is but who gets to decide. A single clock that belongs to the room rather than to either child removes that: the rule is on the wall, and neither of them owns it. Where the age gap is large enough that bedtimes differ, the older one gets a later time by agreement, not by having their own device to point at.
Between the beds, high enough that neither child can reach the buttons from under a duvet, and angled so both can read it. A wall position usually beats a bedside one in a shared room for exactly this reason. Wooden-cased digital clocks with a dimmable display, of the sort listed by JALL, suit this because the numerals stay readable from a couple of metres without lighting the whole room.
The early riser wakes the late riser, and no purchase changes that. What helps is a clear signal that shows when getting up is permitted, and a rule that the early child may read or play quietly in bed until then. Some clocks indicate this with a colour change or an icon, which works for pre-readers. It only holds if the adults hold it, including at ten to six on a Saturday.
If one child is a light sleeper and the other talks, gets up, or comes home later from an activity, a low masking sound helps the light sleeper considerably. Keep it quiet and place it away from either bed rather than beside a head, and never inside a cot if there is a baby in the room. Loud continuous sound all night in a child’s bedroom is a fair thing to criticise, and the answer is a low level rather than a different machine.
There is one honest exception: a teenager with an early start sharing with a younger sibling. At that point the older child needs their own quiet alarm, ideally a light-based one or a vibrating pad, and the room needs a plan for dressing elsewhere. That is a specific fix for a specific clash, not a general case for duplicating everything.
Curtains that actually block the light, a rug that muffles footsteps, and a door that closes without banging do more for two children sharing than a second clock will. They are also the changes that survive the children swapping beds, growing up and reorganising the room, which happens roughly every eighteen months.