[The Might]

Interesting find Findegil, nice idea, I guess that pretty much explains it.
Appendix D does indeed provide us with interesting information about calendars, but not about clocks, or on how they actually worked. I would assume they would be similar to older clocks from the past centuries, at least in the Shire, but it seems that their creation remains a mystery.
Anyway, I personally think that this took place some time after the creation of the Shire, after the Hobbits' lifestyle became more quite and peaceful.