I took several suggestions and combined them and still have some ideas on stand-by to try next.
I took him to the vet for his shots/check-up and the vet said that if I don't see some improvement with the meds he is on, which are for behavioral purposes more than anything...than we will take him off of them. So I have been DILIGENT in making sure I give him his meds EVERY morning without fail so that I can really see whether the meds are helping or not. Sometimes he pees in the floor once a day, sometimes he pees in the floor once every 2-3 days...so that is improvement over 1-3 times every day!
I also changed litter boxes and took down the gate. I am using 15 gallon rubbermaid totes with a hole cut in the lid. Brinkley can't get in them, and so far the cats seem great with them.
I love them because there is VERY LITTLE tracking or litter mess!
If these things don't seem to help in the next month or so, I am going to attempt to cover the carpet area that he is wetting on with the plastic runner stuff...ya know, that you put in the travel areas of your carpet?
Maybe it will deter him from that spot...maybe it will make him move to another...but it is worth a try. The wee pads did not deter him...he just pees on the wee pads now...which IS better than my carpet..ha ha..
My last resort is to get a second opinion from another vet...which I am very hesitant to do. I feel like my vet has done the necessary tests etc...and I trust him. He seems as baffled as me...so I feel like a traitor getting a second opinion...I wish HE would suggest it...that would make me feel better..ha ha..
If you haven't seen my post in the other thread about me "catching" him getting ready to pee on the floor the other night...it pretty much convinces me that it is behavioral more than something "wrong" with him. When I sat up to catch him getting ready to squat, he turned and saw me and sauntered off towards the litterbox and took care of his deed in the right place...he KNEW it was wrong!
That is the aggravating part, ya know?!
Anyway, thanks again for asking...it is nice to know that others are helping me solve this problem...I have gotten lots of great hints and advice beyond making sure the litterbox is clean...