Let me preface by saying I love my beta/biothane harness SO MUCH.
But yeah, black tack… Sigh… It’s an artform. Like most everyone else, a damp rag is your friend. I generally only clean off the tack with product every few days, typically the effax cleaner with mildew resistance and for conditioning, Bee natural/Rudy’s because it also has mildew protection. I’m in the humid South AND my tack is in a tack room that is a glorified tedshed. Mildew is the default setting. Since I started using both, I’ve noticed that there is a lot less green going on, so yay for that.
Other products I use on tack as needed, all inspired by presentation harness preparation (the average driver is waaaay more obsessed with clean tack than the average rider).
Pledge on patent leather, but I’ll wipe it with food grade mineral oil if there are any scratches and then buff it down.
Feibings black saddle soap if leather gets a bit used or rough looking, but you need to let it cure a bit if you use it on the seat.
Black parade gloss boot polish. So far I haven’t used it on my boots, but I’m sure I will soon enough, I just hadn’t thought of it until now. I got it to use on the parts of my Euro collar (harness) that I want to have a more patent leather look and I started using it on the cantle of the saddle. This is pre competition only.
Clear polish quick application thingies. “Black dyed leather needs polish” is the mantra for harness and boots, so why not riding tack? But black polish can be a challenge to white breeches and dun fjords so I use the infused clear polish sponges to put a rich protective finish on the saddle and the entire “top” of the harness, usually once a monthish and/or pre competition
I avoid brass, but if you have it, Wizards metal polish cloth (wadding) is your only hope. A tiny bit torn off does all the brass on a harness so a box of washing goes a long way. But it’s insanely good for all metal so probably would do a great job on bits as well.