In that case a quartz watch or even your cell phone will serve you fine. A $10 Casio digital watch will give you more accurate time than a $20,000 Rolex. And indeed that cheap Casio watch is exactly what Bill Gates wears -- he want merely an accurate timepiece and he has it. But his friend and bridge partner Warren Buffett wears a gold Rolex. To each his own.
People talk of the "Industrial Revolution" but in fact there were four. The first was the technology of time-keeping -- storing energy in a coiled spring and then regulating its release through an escapement to give some semblance of accurate time. That's what all these non-quartz watches do. It's a miracle of precision engineering that they manage to be accurate to within a few seconds a day (of course quartz beats them hands down but's that whole different tech and a whole different story). The development of this technology took place over centuries and quite a few prominent scientists were involved in its development -- Galileo and Huygens among them. Every time we open the case back of an analog watch we see all that thought expressed in material form as well as all the precision work of craftsmen. On the other hand, when we open the case back of a quartz watch, we don't see much of anything, and the little we see is not beautiful.
In terms of accurate time-telling, non-quartz belongs to a bygone era. The "Quartz Crisis" of the 1970s was all about Japanese firms like Seiko and Citizen bludgeoning the Swiss watch industry to its knees. That Swiss industry has never been the same again. Prior to the '70s, Swiss watch firms like Patek used to advertise how accurate their timepieces were. Now they advertise what a status symbol they are. Indeed the whole Swiss industry is selling either status or nostalgia for a beautiful technology and craftsmanship that existed before quartz upended it.
As status symbols go, watches like Patek are close to the ultimate. The Dalai Lama has one. Queen Elizabeth II has one (as well as a Jaeger Le Coultre). A Patek says you've arrived. If a Rolex might be found on someone who flies business class, a Patek might be found on someone with his own jet.