Qualifications
If you wanted to, right now, you could shout, "I'm a horologist" and nobody could tell you otherwise. This is not one of those positions for which you need a degree, a certificate, or even a sidekick who does a slow clap for you (although it's always nice to have one of them).
There are, in a certain sense, levels to horology. That is, there's a certain upper echelon of horologists who trained at high-end schools and cater only to a wealthy, exclusive clientele. We suspect they're also the most likely practitioners in this field to insist on being called horologists.
While technical mechanics can be learned at any vocational school, watchmaking as a higher art is taught on a narrowly selective basis. There are a whopping eight schools in the entire country where you can learn about watchmaking, and their entry qualifications are steep.
Only three of those schools offer the hoity-toity Swiss American Watchmaker Training Alliance certification, and they only dole out a grand total of forty-two graduate certifications for the entire country each year (source).
If you manage to get in at one of those schools, you can expect to tinker and dinker until your hands start to shake. Which means there better be an awesome Swiss-chocolate-y reward at the end of the semester.