You are right. 'Butt' is a singular noun and refers to 'one unit', as you say. 'Butts' always makes me think of the running joke in The Simpson's, where Bart makes prank calls to Mo's Bar asking for people with silly names. In one episode he gets the bar owner to call out 'Seymour Butts! I wanna Seymour Butts!' And if anyone here wants to know when it IS acceptable to write the dreaded 'w' word, well, there's an example. When quoting cartoon dialogue, even a stuffy old schoolma'am like me is happy to write 'wanna'. But back to the butt: if you want a plural word to describe what you are showing when you are mooning, try 'buns'.

yes, my buttocks, my butt, but not my butts

If you want to talk about your "butt" individually, you would say "butt cheek". Example: My left butt cheek and my right butt cheek. It's slang, but it's what I'm used to. Also, you can say my butt cheeks. Some people spell it "butt cheek", and I've also seen it as "butt-cheek". Hope this helped! -Kyle