Can a person wear a gold mecahnical watch on shabbos even though it has stopped ticking or it never was wound to begin with? It’s not necessarily for time. Can a person wind a mechanical watch on shabbos?
If a person wears the watch as an item of jewelery, irrespective of its ticking or being wound up, then it is permitted to wear on Shabbos (even in the public domain), both if the watch is moving and if it has stopped. As a part of a person’s wardrobe, wearing the watch does not involve an act of ‘carrying’.
It is not permitted to wind up a mechanical watch on Shabbos.
Sources: The Chayei Adam (44:19) rules that winding a stopped watch is prohibited because of tikun mana, an act of repair, and therefore a Torah prohibition. This is a chiddush, because the watch can hardly be said to be ‘broken’ in its stopped state, and some poskim have therefore disputed this logic (see Panim Me’iros 2:123; Ya’avatz 1:41; Kesav Sofer 55; Sho’el U-Meishiv 6:53). Yet, the general concensus is that there is at least a rabbinical prohibition involved in winding up the watch (see Da’as Torah 338:3; Minchas Shabbos 80:241), and as the Mishnah Berurah (338:5; see also 252:50) rules, it is therefore forbidden to wind up a watch. This is also the prevalent custom (see Kesav Sofer 55; Minchas Shlomo 9). Interestingly, according to the Chazon Ish (Orach Chaim 50:9) winding up a watch is considered “bringing it to life,” and prohibited on account of boneh (much like electricity).
Concerning wearing the watch as jewelry, see Biur Halachah 301, who is stringent concerning watches because people don’t wear them when they’ve stopped. If the watch is worn even when stopped, the Mishnah Berurah will concede that one may wear it both when moving and when stopped.