How do you teach someone an attention to detail, good work ethic, and perseverance?

Those are character traits, not methodologies. If a PM has those 3, he'll be a good PM regardless of anything else. Actually, if someone has those 3, they'll be a good anything.

Agile or something else might make someone better, but they can't determine if someone is good.

I feel like shop work ( saws, sanding, filing, etc ) and music are better for that but maybe that's bias. Sports teaches some things, but there's an awful lot of sorting going on and some of the "adults" have weird reasons for being there. But I think of character as "what you do when nobody is looking."

Truly great coaches are worth it, though. The best one I ever had told me to get out of sports :)

If Zen and the Art of Motorcycle Maintenance isn't required reading anymore, this could be a sign that it should be.

Besides. Things like Agile aren't "observing what people who are good at what they do, do". It's a formalized process based on the ideas that some people who are good at what they do have about WHY they are good at what they do. But do people who are good at what they do really know why they are so? They probably don't! Besides, they are going to mix in all kinds of things that they think they do, or they think they should do, or they think that good people they learned from did, in that formalized process. In the end, the process they describe may sound good to them, but have very little to do with what good people actually do or should do in any particular circumstance.

Not everyone can be 'taught' or just go by a structure. In fact I would strongly argue that those who just go by a predefinied step-by-step structure are always never the 'good' ones.

The question isn't whether it is possible to teach it, but whether it is practical.