OP, you have gotten lots of good advice here. Perhaps I can add to that.
Background: Electrical engineer with BS, MS, PhD. I grew up on a dairy farm. I'm 51 now. Besides EE courses, I took many not-required classes in ceramic engineering, physics (optics, astronomy), and geology. I had a BROAD education, and this is important. The "extras" I took were quite material and practical compared to the stereotypical "dry" EE classes. I have had career uses for ALL of this. As a philosophical approach, soak up ALL of the education you can get your hands on. No one can ever take it away from you.
Math, and math in engineering - there are kinds and levels. High school math (algebra, geometry, trig, basic calculus if you can get it) are highly useful in one's career. "College-level" math - it depends. Some engineers use hardly any math doing engineering; they may run software extensively. But the math gave them the knowledge of what the software is doing, and some notion of when it might be lying to them (as long as they don't trust it unquestioningly). Others use math extensively (I do in my current job) at the derivation and/or high calculus level. By the way: accounting is "just" arithmetic, but some knowledge there will be very helpful. Finally, I had a poor (not really taught; no teacher) math senior year in high school - still got a PhD in EE, in electromagnetics. LOTS of vector calculus.
Engineering and degrees - others have said this. The degree is a gate-keeping criterion. GET A BS (this will usually be better than a BA, at least in the beginning). There are lots of successful blue-collar folks, but it's complicated: it has a lot to do with where they live/work, the time they started, what they do, and the opportunities they had earlier in life. This ALSO holds true for the BS degreed person. There is a certain amount of right-place, right-time, carpe-diem stuff - no one has every jot and tittle planned out. Also there is no such thing as zero-risk. LIFE has risk, including the so-called "sure thing" or "sure path." Realize this and deal with it.
Working for a company vs self-employment - this is a personal choice, tightly coupled to risk. Lots of folks look at self-employment as freedom, but it's a tough row to hoe. It's harder economically (mostly due to tax structure). One person has to do everything - marketing, accounting, sales, plus the "actual work." Sure, you can outsource some of that - for a price. That leads into...
Non-work-related tasks - This is everything that's not your passion (not gunsmithing, in your example). I got very little training in those other tasks mentioned above, and had to learn some of it over the years the hard way; I work at a small business, but I worked most years at several different large businesses. You have to seek out knowledge in these other areas. You can take classes, or learn while apprenticing, or whatever - but ignore them at your peril.
Finally, regarding ME specifically - I've done many ME tasks in my career. There is a surprising amount of commonality shared amongst the engineering subdisciplines. In my current (small) company, everything is important - but I can see that machining/fabricating, 3D CAD, materials, thermal management, and manufacturability are all very important. I can do or contribute to some of these. People who can do some or all of these well, should always be able to make it. And "making it" may require being flexible with where you live (where the jobs are). As an example: my specialty is RF/microwave. I can't live just anywhere and do that, without substantial travel or building a consulting business from the ground up (using my network, of course), unlike someone who is a civil engineer, or accountant, or nurse, or...one of quite a few occupations that are used everywhere. Something else to consider.
I realize that this is long and contains many separate, often very different, topics. They are some of the things I think of when looking back on my career and asking myself what I lacked, or what I would have done differently (THAT would be a long post too
), or what I might do in the future. Best of luck to you. And you might want to consult some engineering and career fora as well.