This definitely falls into the 'incontinence' category rather than 'inappropriate behavior'.
I did some research on this in cats and it doesn't seem to be something that is extremely easy to deal with or treat. Finding the cause was the number one point in every article I found. I'm thinking your vet was probably right on target with the neurologist. I did find a few references to possibly being able to treat the problem with surgery or antidiarrheal products, but in your cat's case, diarrhea is not the issue.
I was going to suggest adding a second litter box to the house as some cats want 2 litter boxes - one to urinate in and one to deficate in. I was also going to suggest feliway plugins as they are excellent in helping to change inappropriate behavior patterns. Your kitty definitely appears to have a physical problem, and I think the neurologist is going to be the best choice at this point. They do have "stud pants" for cats to help with cats that spray, and they may be somewhat useful in helping keep the stool off the floor, but ultimately, they aren't going to solve the problem.
I wish I had some alternative suggestion that I could give you, but in this case, I believe further testing is all that can be done. If you decide to take him to the neurologist, I would be very interested in knowing the diagnosis and prognosis for your boy.
I really don't; however, I am going to refer this onto some of our veterinarian experts on the site. Hopefully, one of them will be able to provide additional insite for you.
Hi again! I checked with our vets online and was offered the following information. Hopefully, it will be beneficial.
Things to do before going to the neurologist - have the cat seen by your regular vet & have them do a rectal exam to evaluate anal tone and also anal glands for infection in case this is more a case of inappropriate elimination due to pain and avoiding the litter box. Also check tail tone. Also, x-rays of the lower spine to check for impingement on the spinal canal perhaps from arthritis changes.
If these things have been done, and your vet still has no idea, if you go to the neurologist, all you will be is commiting to at this point is the cost of the office call. Ask the neurologist what the possible causes are, what tests are needed to sort them out and how much these will cost, what the potential treatments for each of these are (and the cost of the treatments) and success rates. This should help you decide how to proceed. Bring a copy of the record and any lab test results or x-rays with you to the neuroloist to help keep your costs down.
I think this should at least give you a direction to go in and the appropriate questions to ask. Please let me know what happens with your kitty.