A good, out of character conversation is always a good place to start.Consider the players real life personality when going in. That is going to shape how moving forward looks.
I recently ran a game with two kids that were a little difficult. One was was a kid who could be distracted by lint(ADHD, but I don't know if he was actually diagnosed), and the other was a kid who was on the Autism Spectrum. He was an almost extreme stickler for the rules. Needless to say this is breeding ground for potential problems. The ASD kid sounds, in my mind, kind of like your player.
So how did I deal with this? I made my expectations very clear at the outset. Since the ASD kid was new to our group, I took the time to remind all of my players that we were there to have fun.
My play style is to use the rules as guidelines because with RPG's, the most fun happens when you try to make sure the story trumps even bad rolls and that I am more than willing to let players wander outside the scope of the mission, so long as they understand that I am going to change from dignified DM to demented kitten if they go too far afield. With this in mind. I borrowed something from a gaming buddy from way back in the past...Structured, funny, fail roll results.
If a roll is a miss, but it's close, I try to throw a little positive the players way (you nicked the goblins helmet, it rang like a gong , and is now facing backward on his head) If it's a critical fail, I try to make the result not only bad, but ridiculously so. An example is when one character missed with a fire spell but he was near a bunch of brush. He set the brush and therefore, his hair, and I made the character run around for 3 combat rounds trying to put his hair out. I keep the critical fails humorous when I can. I also let the players try to use the fails to set up future actions based on the fail. I don't really know how to explain this, but an overly simplistic description is like "you miss with your mace swing, but if you continue the swing in a full circle you might either get hit in the back, or I'll give you 1.5 times damage if you hit on your next pass" They can turn a failure right now into a potential win in the next minute or 2. Fast, positive, feedback. I'm guessing your player may switch moods pretty fast. keep the feedback loop going. If the mace misses the second time, give him a chance to do a Dex check and start break dancing. He now has something to look forward to, to stay engaged with. With luck, after a few situations you set up, he will start setting them up on his own.
If the rest of your group can get behind this kind of outlook (and you will have to be the judge) and your troublesome player is alert to this, you might be able to create an environment where everyone can have fun, and you get a lot less dead-heading.
It seems to have worked for me, We all have fun, and every now and again, a nat 1 is nearly as satisfying as a nat 20.
Hope you get this sorted to where everyone in your group has a good time. Game groups too hard to find to let one fizzle. Best of Luck