My butt hurts from sitting on my stool for 7 1/2 hours a day, 4 days a week at the gunsmithing school I'm attending right now. Not that I'm complainging, it just takes some getting used to. Busy work is a lot of the work you may and will have to do as a gunsmith, tedium is the norm. I constantly hear belly-aching about how long it takes to do one project. I just spent 12 hours making a Model 12 fore-end wrench. At $10 an hour its an expensive wrench, but $10 is extremely generous in this business as has already been pointed out.
Making tools is part of the job, because sometimes you either A: need the tool now and cant wait for it to be delievered or B: they dont make the tool you need.
Dont think you can do everything on a mill or lathe either, making hand-fitted parts for old guns happens more often than you might think.
If you are mechanically inclined you've already got a toe in the door, have any experience properly working with power and hand tools and you've got a foot in the door.
The most important thing though is to constantly study firearms and their design and function. Knowing how a gun works speeds up the trouble shooting process since you're able to diagnose the problem. Not knowing how the gun works properly and being handed a gun that needs repair takes a lot of reverse engineering and considerable research. Even then you might not know exactly what's wrong with the damn thing, trust me I know, I've had it happen more than once and I'm not even near professonal level.