I have a 4 year old neutered male cat that has a penchant for peeing where he pleases. First, as a young kitten, it was in a heat register. Then in my laundry basket (clean) whether there were clothes in it or not. Next, at about 2 years, he targeted my recycling basket (about 3 to 4 inches tall) under my desk that I used for paper only. These incidents were infrequent; once or twice. At one point, he peed in the plastic bowl that I kept all the toys in. He recently gotten in our closet and peed on a pile of folded clothes on a shelf. The latest incident is that he climbed into a hamper of discarded (wet or dirty) towels that is kept in the bathroom.
He is a very sensitive boy. He makes you feel like he lacks self confidence. He can be a loving cat, but only towards myself and my husband. He and his brother, and our older cat, make themselves scarce when we have company, which is not very often. We have never noticed any behavior differences after any company.
When some cats sends pee-mail as yours is they may not be feeling well physically. Or due to a change in their environment or the humans around them their psyche gets knocked out of sorts for a while and they act out. A perceived territorial infringement of another cat in the house or within eye or ear shot outside will get them spicing up the household as well and a cat more sensitive by nature is going to be more susceptible to all of the above. It’s usually one or the other but there’s no reason they all can’t be and that you’ve got a cat sampling from the whole buffet.
If this were solely due to his being a sensitive cat I’d be tempted to look at some kitty Prozac which seems to work for a lot of cats. There are some other treatment possibilities for this as well, exercise (good luck), mentally stimulating toys, and naturopathic treatments but you really should find someone in your area to work with and narrw things down.
Maybe he’s just adventurous. It’s almost like he finds something somewhat litter shaped and thinks, “Oh my isn’t that exotic, I just must have it.” and then he does. I’m worried that if this is the case it’s going to be a tough row to hoe to get his butt back in the pan. It’s a matter of conditioning and the best way is to populate the rooms of his indiscretion with litter pans so that he gets his head back in the game. Once it is, I’d keep them where they are for another 3 months and then wean him off a little at a time hoping that we’ve reprogrammed him to re identify with what a litter box really is.