You're very welcome, Pam. Sorry to be such a downer. I had some thoughts though, so will offer them and you can see if any of it seems relevant. May not be. But always good to cover all bases.
It is always possible that he's brain damaged, but in my experience even pretty severe brain damage often fails to circumvent mating instinct. Generally that's one of the last things they lose. But if it were a toxicity induced brain damage, i.e. if he swallowed a lead sinker, or ingested a source of mercury, then that could also dull his necessary instincts, everything from preening to mating.
These sources of brain damage are more common and readily available than many think. If there's a shed on your property, and in the past there have been "handymen" working there (mechanics, painters, welders etc) chances are heavy metals and other very nasty chemicals have contaminated the ground around it. Even if the shed floor has been washed... Where did the water go? Batteries leak, many sealants, cleaners, paints and other chemicals are amazingly toxic, even touching some with your bare hands can damage your neurons. They can of course persist in soil for a long, long time, often being non bio-degradable.
Even if it's only able to be measured in parts per million in soil, it doesn't take many ppm of some chemicals to cause severe damage, and with some chemicals it is actually more damaging to be exposed to a tiny amount infrequently than it is to be exposed to a larger amount regularly. A chicken dust bathing in dirt that's had battery fluid spilled in it years ago, then preening its feathers, is ingesting far more than is even vaguely safe.
The pectin in apples is proven to detox heavy metals including mercury and lead, even aluminium and others which are very difficult to remove when past the blood brain barrier. Apple Cider Vinegar (with "The Mother" in it, unfiltered, unpasteurized) in their water should do that for you.
Councils around much of Australia lie about waste and fill just to be allowed to dump it on residential properties; they will "offer" you fill only to charge you to ruin your land. They are amazingly corrupt, I'm sorry to say. If someone tells you something is safe, don't believe them, test it. I currently have the council here telling me the dam is clear of chemicals "from the plant" (Nearby manufacturing plant). But they won't tell me what it's positive for. Mystery deaths have already occurred on this property and I am not keen for more. But they're not keen for more work or lawsuits. So the back-and-forth continues.
Also, sprayed insects can travel far and wide before dying, so even if you don't use chemicals for pest control, your neighbor can be an unintended threat. Some people are amazingly negligent or casual about chemical usage on their land too, and dangers can persist for decades after initial "laydown".
If you want to try with him, I understand; I like to know for sure, or as close to it as possible, before giving up. I want to know "why" so I know whether or not to try with more animals like that individual in future, or just cut my losses... Investigation has its rewards but also its pitfalls. I've kept and bred animals I ought not to just to find out for sure whether or not it was correct to cull. But on the other side of the coin, many times enough they were viable despite appearances, and when I say "viable" I don't just mean "able to breed" I mean "worthy of breeding". And sometimes the only way you will know for sure is if you breed them.
If you want to see if it's hormonally based, giving him a pinch of kelp per day will most likely show you as it regulates the endocrine system. But it may take as long as a year to show the full results. You should see some sooner though. But if you think he's purebred for a certain color, kelp for a year will show you the truth of the matter. It brings out hidden traits which were hiding (dormant) due to the lack of complete functionality of the endocrine system. So he may change color of eyes, skin, beak, legs, claws, feathers, earlobes etc, (everything) and if he were a hen he could even change eggshell color as well.
Kelp makes them smarter, healthier, more fertile, calmer, and disease resistant. Great all-round multi-vitamin and mineral supplement.
If you cull, now, or soon, or later on, even years in the future, I would recommend you do a necropsy and check that he's not deformed inside or has tumors on the brain or reproductive system or any visible anomaly like that. Many poultry keepers have to learn to do necropsies sooner or later, and better sooner because of the valuable information it renders, in my experience. If I didn't start doing "post mortems" or "necropsies" (site tells me both words are misspelled but my browser won't let me fix the definition lol)... Then I'd still be breeding leucosis and some other issues on.
Anyway, just some random ideas, best wishes with him whatever your decision is.