I recently got an old Cinelli Unicanitor saddle with what appears to be the suede covering. Wondering what products I should use to clean it up. Just trying to get off any dirt and grease without damaging the material.

Also, I've done some internet research, but if anyone has info/pithy anecdotes on what exactly I have, I'd be interested.

Well, back in the days when all the pros rode leather saddles, there were people who would modify factory made saddles. One such person --perhaps the most famous-- was an old racer named Giuseppe Ottusi of Milan, Italy. You can find some photos of his work on the internet. He would take something like a Brooks B17 and give it a subtly different shape. The Unica Nitor saddles were modeled on his saddles. They are light, and highly regarded in some circles.

About the only thing recommended for most suede is a small brass brush, available in most shoe repair shops.

I like Cinelli saddles, but the #2 in suede no matter the color is silly in my mind, any amount of riding mats down the suede, and until it all gets matted down especially in black it looks terrible.
The suede does keep on "planted" on the saddle at least with wool shorts butI shift my weight around from time to time, descending etc.

Yeah, suede makes too much friction. I like to slide around on my saddle, regardless of how mischievous that sounds.

I much preferred the old buffalo hide model. Those suede ones never do look good for long. That's a nice looking one, however, OP.
If you intend to ride it, anything you put on it will destroy the look of the original suede.