That bolt on the bottom is the water drain as the manual calls it, its for making sure there is no water in the brake housing after riding through water. The cover has a reusable rubber gasket around it where the bolts hold it on, and there is a seal on the axle as well as the brake lever, its a sealed system, should be dry in there. If you take that bolt out and fluid is coming out its most likely water or someone put oil in there to free up rusty brakes... I have seen it happen.
Pull the right rear wheel off, remove the hub from the axle, remove the axle nuts, and the o-ring behind the nuts, unbolt the cover and pull that off. Get it all cleaned out, a couple cans of brake clean and a wire wheel and clean it all out, remove the brake drum, it slides off the axle and out, clean that up, if its rusty but not pitted badly just give it a light sanding, i like to spin them on the lathe and clean them up, but a wire wheel on a drill and some 120 grit sandpaper will clean it up and give it a little tooth for the brake shoes. The brake shoes are available brand new, however, every pair i have bought recently are oversized, the manufacturers are compensating for what they know will be a worn drum that you can't buy a new replacement for, so i usually end up shaving out a bit on the lathe to clean up the drum and give the proper clearance for the larger shoes. If the shoes are not badly worn or separating, the brake material likes to come unglued and come off the aluminum bracket part of the brake shoe, just clean them up, i just give them a quick clean with some sandpaper then wash with brake clean and put it all back together.
If you take the drain bolt out you can put a pan below it and just wash the whole housing out and let it drain down. Then put it all back together and good to go. The service manual is downloadable and available for free online, has all the steps and info you need.
If the bearings in the rear are getting noisy you have to take everything apart that i mentioned to pull the axle anyway, the axle pulls out to the left, so you have to remove the left wheel and the chain case cover and drive chain as well, then the whole axle slides out to the left. You can buy a kit of the bearings and seals, cheap and easy to do, and just give the whole rear end a refresh. The absolute hardest part of these is if the brake drum won't come off, they are splined to the axle, and sometimes water gets in there and they rust on. If you are lucky it will slide off with a little cleaning and some PB blaster to lube it up, as long as the brake drum comes off your golden to fix everything else and its easy.
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1984 Honda ATC200ES "Big Red"
1982 ATC200E "Hondie"
1988 TRX300FW "Project Quad" Still in progress....