Correcting my earlier post...

[Eric Oppen]

No: HPFGUIDX 53200

Okay, I went back to the Texts (I fear movie contamination) and found out
that yes, on the Rock Harry was finding out about the exact,
down-to-the-minute time the night before his birthday by seeing _Dudley's_
watch, not his own.  *slams ears in car door to remind self to Always Check
The Texts next time*

But, at some time between then and the later books, Harry acquires a watch.

Could that have been Hermione's Christmas present to him at some point?  A
watch?

The more I think about it, the more reasonable the idea seems.  Hermione is
Muggle-born and more used to watches than, say, Ron, and is _also_ more
aware than Ron is of which Muggle artifacts do and do not work well at
Hogwarts.  Her parents are dentists, which means that they aren't shy a few
bob.  Could she have asked her parents to use some of the money they'd
earmarked for her to buy Harry a _mechanical_ watch, even possibly
second-hand?

We've seen very little of Hermione's parents, unlike Arthur and Molly
Weasley, but I think from what little we know they'd probably be just as
sorry for Harry, and just as indignant about his life with the Dursleys, as
Molly Weasley is.

I don't know how much an inexpensive mechanical watch would cost these days,
not having been in the market for one, but I don't think that this is
something that's totally out of the question.  Looking in the second-hand
market would also bring the price down considerably, and remember, we aren't
talking about the fanciest Rolex on the market.  Just something to help
Harry get to classes on time.