Desire. You either have it or you don't. It gets you to where you need to be and keeps you there.
Good timing. If you are out there all the time your timing is likely to be better.
Good luck. As the old saying goes.. you make your own luck. I think this is about half true.
Willingness to hunt somewhere that you don't really want to hunt because it is where the type of deer you seek lives. Don't fall in love with an area that does not produce the size of deer you seek. If you do you will never know if you are good, and no one else will know either. A poor hunter in a good area will look a lot better than a good hunter in a poor area. I said "look." Every mule deer book will tell you to go where big bucks grow. Good advice if you want to kill big bucks, but it does not automatically make you a better deer hunter. You will damn sure look better in the grip and grins though.
Be a good shot on game. There is no sense in missing when everything comes together. There is nothing worse than listening to a" the one that got away" story, and not know if the hunter knows what they are talking about.
Don't spend too much time dwelling on becoming a "good" mule deer hunter, because in the end you can't measure it. If you turn it into a competition it will take the fun out of it.
There are some damn good mule deer hunters who have never shot a truly big buck, and some damn poor hunters that have.
If you really want to be good have your deer tooth aged in a lab so you know what you are talking about. Big deer aren't always old and smart, and old and smart deer aren't always big.
These are all just opinions I have formed over time. I share your desire to become a good mule deer hunter and if I ever actually figure it out, I will come back and update this post.