So make reasonably sure it's the diff first, disconnect the driveshaft and see if it's still notchy when you turn the flange. If so, go ahead and drop the third and verify the gear ratio, then start searching your classifieds and Craigslist. You can also search the Fore Sale sections on Yotatech, IH8mud, and Pirate4x4.com. Any 8" third member with 4.10 gears will work - you'll see a lot of talk of "4cyl" and "v6" diffs, ignore it, that's all completely irrelevant for your purpose. Any 4Runner rear diff with the right gear ratio will work, up to '02 (and maybe farther, does the 4th gen have an 8" axle?). Early pickup rear diffs will also work, but at some point Tacomas started getting the 8.4 rear axle and I don't think that third will bolt up? Post up the ads you find and we'll help you make sure it's the part you want. Aim for $100, that's roughly what they'll go for though you might get lucky. If you're in a hurry you'll pay a little more at a junkyard, sometimes $200-$300 but if you need it
right now that's an option. For a little piece of mind, you can take whatever third you find to a driveline/differential shop and ask them to check it out for you, they'll probably charge you a couple bucks but they'll make sure the backlash is in spec and the gear pattern is good.
Removal and installation is very straightforward with basic tools. Soak everything you can see in PB Blaster a couple days before you start, and then again a couple hours before you start, and stuff should come off easy. First make sure the fill plug is free, I think it's a 19mm, because if you drain the oil and then find out you can't fill it you'll be pissed and teach yourself new swear words. Then drain the gear oil, that's a 22mm? 24? Somewhere in there anyway. Put the axle on jackstands, remove the wheels. Unfasten the ebrake linkage behind both brake drums, then remove the brake lines, 10mm if memory serves and you absolutely want to use a flare wrench, do not strip those or again with the swear words. Four nuts on the backside of the drums hold the axle shafts in place, should be 14mm - take those nuts off, then slide the axle shaft straight out, being careful of the rubber seal at the end of the axle housing, don't rest the shaft's weight on the seal? Pull the shafts out, rest them on the lug studs with the shaft pointing up - be careful, they'll be slippery with gear oil. Unbolt the driveshaft from the pinion flange, those are 14mm. Rest the free end on the ground. You can leave the other side connected to the tcase output, but don't let the shaft come apart at the slip coupling. Now unbolt the third member from the housing, this is a bunch of 12mm? nuts in a ring around the edge of the third. Take them all off then give the third a couple very stiff whacks with a rubber mallet, it should pop free. Lower it carefully, it's heavy. Installation is the exact reverse except you fill the third instead of draining it

, you'll want some brake cleaner to clean the surfaces between the third and the housing, you can use Permatex's The Right Stuff instead of a paper gasket, and it may help to have somebody jiggle the pinion flange back and forth as you reinsert the axle shafts.