Is it possible to teach an older horse stall manners?

I'm not sure that you can teach them - some horses are just naturally cleaner than others. If your gelding hasn't been in a stable before he might be quite stressed by the situation, so he's making more mess, and he may in time calm down and not make such a mess. If he decides he doesn't like lying down on wet bedding he might make an effort to be cleaner too. If he's a flighty sort though he may not change.

What you are bedding him on may also make a difference. Our gelding was a nightmare when we first got him, he was completely trashing the bed every night (he's out during the day, stabled at night) - muck everywhere and soaking wet, and we were using a new bale of straw virtually every day. Eventually we got fed up and changed him onto shavings, and he immediately became much cleaner - only 3-4 piles of muck as opposed to 10 or so, and one neat wet patch in the middle. We came to the conclusion that he didn't like the straw, and was also eating quite a fair percentage of it.

Worth remembering that whilst a mare can pee in a corner (or even up the wall!), a gelding can't, he's going to pee more in the middle of the stable - it's just the way he's built!

Horses don't learn stall etiquette in the sense that you are thinking of. They don't learn to do their business all in one area. That is something that some horses do naturally and some don't. It could well have been both of their first times in a barn or they could have both lived in for years. No way of telling.

You re just going to have to deal with his mess.

There is such thing as stall etiquette though. This includes things like not crowding you when you go in with grain, walking in slowly with you and not rushing and going into the corner when someone comes in (this is especially good because it means that if there is an emergency even a nonhorse person can safely feed the horse). This is all basically groundwork and is taught through consistency and reinforcement both positive and negative.

You can't. No one taught your mare stall etiquette. She just happens to be a very neat horse. Some horses are pigs, some are very tidy.

Stallions like to go in specific areas to claim that area as "theirs." I know mares AND geldings who are pigs, and I also know mares AND geldings who are neat freaks.

Just suck it up and clean his stall.

stress could be a factor. I seriously doubt a horse can be potty trained.

I would like to point out a tidbit of information. It is a common trait for stallion mustangs to establish a "dumping station" in one area in a pasture or paddock. This is their way of marking that this territory belongs to them. We have a blm adopted jack burro that does this as well.

Some horses are clean and some are dirty. My mare actually likes to roll in poop. It disgusts me and she smells all of the time, but it's what she likes to do.

In our own experience, mares are "neater" in their stalls than the boys. Dunno why. Maybe it's like what Charles Schulz captured in the Peanuts strip with "Pig-Pen" who could raise a cloud of dust on a clean street--girls are inherently neater than boys. Or maybe not.

Well, that's just being lazy.

So you want to teach him to poo and pee in one corners so it's easier to clean up? Well what about your horse? I don't think they like having to go to a specific spot just to go to the bathroom. That's selfish and lazy on your part. Let your horses go where they want and get used to doing the work.