Well, if I can pull this off with ASCII art, here is how I envision our clock's PLoT on the ULoT (universal line of time! )


Code:
ULoT     1           4                  2    6    
|-------------------|-----------------|--------/
                                        
|-------------------|==================|--------/
PLoT                 |        5         |
                     |                  |
                     |                  |
                     |~~~~~~~~~~~~~~~~~~|
                             3

1. Span of time which only 1 Watch exists in timeline.
2. Point in time which Loverboy buys Watch.
3. Watch traveling back in time with Loverboy.
4. Point in time which Loverboy arrives in the past and sells Watch.
5. Span of time in which Watch exists twice at once.
6. Arbitrary point in time which only one Watch exists in the ULoT again.
IMO it looks really horrendous, and I tried to color code it to make it more eligible, but if it's still confusing, I understand.

Anyhow, that attempt of an explanation is how I see the watch existing twice at once, yet being the very same watch, and not two different watches. One point of evidence could be, assuming dynamic paradoxes could be done in this example, should the younger watch be, say, destroyed, the second watch would cease to exist as well.

Also, along the indication that the older watch would obviously be more aged than its younger equivalent, here is an excerpt that may be interesting to read:

The philosopher Kelley L. Ross argues in "Time Travel Paradoxes" that in an ontological paradox scenario involving a physical object, there can be a violation of the second law of thermodynamics. Ross uses Somewhere in Time as an example where Jane Seymour's character gives Christopher Reeve's character a watch she has owned for many years, and when he travels back in time he gives the same watch to Jane Seymour's character 60 years in the past. As Ross states

"The watch is an impossible object. It violates the Second Law of Thermodynamics, the Law of Entropy. If time travel makes that watch possible, then time travel itself is impossible. The watch, indeed, must be absolutely identical to itself in the 19th and 20th centuries, since Reeve carries it with him from the future instantaneously into the past and bestows it on Seymour. The watch, however, cannot be identical to itself, since all the years in which it is in the possession of Seymour and then Reeve it will wear in the normal manner. It's [sic] entropy will increase. The watch carried back by Reeve will be more worn that [sic] the watch that would have been acquired by Seymour."

On the other hand, the second law of thermodynamics is understood by modern physicists to be a statistical law rather than an absolute one, so spontaneous reversals of entropy or failure to increase in entropy are not impossible, just improbable (see for example the fluctuation theorem). In addition, the second law of thermodynamics only states that entropy should increase in systems which are isolated from interactions with the external world, so Igor Novikov (creator of the Novikov self-consistency principle) has argued that in the case of macroscopic objects like the watch whose worldlines form closed loops, the outside world can expend energy to repair wear/entropy that the object acquires over the course of its history, so that it will be back in its original condition when it closes the loop.
Although it doesn't directly pertain to this scenario as Loverboy is not buying the same watch he sold to the pawn shop years before, but rather buying a younger version of it and sending that one back in time.