Odds of Getting In
Since anyone with a tiny light and a tiny screwdriver can claim to be a horologist, the bar we're setting here is whether anyone would ever employ you as one. To get a job with a watchmaker, or at a jewelry store, or other specialized accessory shop, you'll need to have some kind of apprenticeship or degree program under your belt.
If instead you're amenable to just working on clocks and watches as part of a general handyman-style service, your profits should correlate well with your ability to get the job done. There aren't a lot of professionals out there—only about 2,000 or so in the whole country—so if you're good at the little details, you'll be fine (source).