a uita is etymologically related to English oblivion, so forgetting is the primary notion. The idea of forgetting oneself by staring motionless at something could explain the origins of the reflexive usage se uita meaning looking: "I forget myself at the clock" :-)
Yes, we typically use "ceas" for both, but I seem to recall "ceas de perete" being used for a clock hanging on a wall (perete) and "ceas de mână" for a watch. Also, "orologiu" for a clock that is affixed to a building, such as a tower clock; "pendulă" for a pendulum clock; "clepsidră" for houglass.
It looks like sometimes they were called "clepsidre cu nisip" in Romanian ("nisip" = "sand"), I'm guessing to differentiate them from the ones using water, ground eggshell or marble:
"Clepsidrele cu nisip mai erau numite și nisiparnițe (arhaism)." = "Sand hourglasses were also named nisiparnițe (archaism)."
Ceas: From a Slavic language; compare Common Slavic *časъ (“time”, whence Russian час [čas, "hour; clock; time"]).
The Common Slavic root comes from Proto-Balto-Slavic *keʔs-, probably from Proto-Indo-European *k(ʷ)eh₁s-. Cognate with Old Prussian kīsman (“time”) and possibly Albanian kohë (“time”). Akin to *čajati (“to wait, expect”) and *čakati, with a semantic development similar to the one found between *godъ and *žьdati (“to wait”).
The other possibility is from the lengthened grade of Proto-Indo-European *kes- (“to go”), with a semantic development similar to the one found in Latin annus (“year”) (< earlier *atnos < PIE *h₂et- (“to go”); compare Sanskrit अटति (átati, “to go”)).
Edit: I got it all wrong. I thought you were asking for ceas.
Actually, that doesn't sound Slavic at all to me, probably because of the ending "idra," which makes me think of "hydra" that has a very strong association with "water" (it means "water snake"), which makes sense since "clepsydra" means "water clock."
"clepsidră" = "clepsydra" comes from from Latin clepsydra, from Ancient Greek κλεψύδρα (klepsúdra).