"He is wanting a watch."
Translation:Tha e ag iarraidh uaireadair.
This sounds totally plausible. A similar word, uaireadóir exists in Irish. MacBain suggests it comes from *horatorium? where the * and ? are his, so basically he is guessing that it comes from an unknown Latin word.
But -torium in Latin means 'a room' so that is not very likely.
My guess is that it is formed the same way as the time-er that you mention. That should be *uairear. Just try saying that and I think you can see why they put the d in?