Question...should the gate be unique because of its latch only or because you have carved (or afixed) an interesting bas-relief onto the gate itself? Could you perhaps use the old time 'round rail loop ketch' common to cattle/horse fencing as a gate fastener? This method would leave the front of the gates free for a continuous, creative carving that could cross over both gate sections. Or could be panels with copper inset designs, something from nature or modern look. Or just carved panels. Searching bas-relief art may give you some ideas. As to a regular latch idea which could be different...what figure can you carve that fits the hand well and can be used as a sliding bolt? A cat chasing a rat? Something like that. Whimsey, maybe? Or, recycled metal pieces or old tools, reworked.

I love cabinet locks especially on the upper double stacked cabinets. I have only seen them used on inlay cabinets. Can they be installed on overlay cabinets?

Bull pucky. Gates get installed all the time with doorknobs and or deadbolts. You have to know the final thickness of the gate- at one of my rentals the gate is a 1 1/2" thick frame plus 5/8" boards so 2 1/8" overall, the trick is to buy a knob or lock that work with that thickness. Not hard at all. You cannot use an electric keypad (with a battery) as they will not hold up, but a mechanical keypad will work great.

Double pocket door latch? Double Pocket Door Latch David brings up a good point about the cat being able to slip out the bottom so might not work. Years ago when I had a cat and a dog, they teamed up to escape out the back screen door. The door had a lever handle. The cat jumped up on a piece of furniture that was by the door. She was able to depress the lever to unlatch the door while the dog nosed the door open. Out they both went! They were quite the team. I started noticing bits of red yarn on the floor near the Christmas tree. After a few days, I noticed that my homemade gingerbread men were disappearing from the tree. Finally caught them in the act when I found the cat way up in the tree. The cat had been knocking the gingerbread men down off the tree; the dog promptly cleaned up (most of) the evidence. All but the red yarn that I used to hang the gingerbread men!