The later Beavers have a standard rotation PTO, though some earlier versions have a counterclockwise output. I have a Satoh 1440, very similar to the Beaver, as well as a 186D. I know you have largely dismissed the Beaver. From what you've said the seller is asking, compared to its condition, I think you're making a good decision.
The 186D is a good tractor, and I like mine. It is built very solidly. The Powershift is what makes the tractor, in my view. A hydrostatic transmission may offer more adjustment within each range than the Powershift, but the Powershift is a couple steps ahead of a straight gear-only transmission. I have said elsewhere that without the Powershift, my 186D would be useless. That's obviously not completely true, but it isn't a terrible exaggeration.
The 186D has a very powerful 3 point hitch and hydraulic system and will lift and handle implements a couple sizes larger than what its power will let it run. Mine rockets a heavy-duty 4 foot brush mower up and down, and would probably take a 6 foot machine fine too. There is no way it would run the cutter, though. My 4 footer will commonly bog it down, even just cutting weeds and grass in my orchard.
I think the 186D is underpowered for its weight and commonly used applications. It is rated only 1 hp higher than my Satoh 1440, but weighs significantly more. Mine, with all its ballast and additional weight, will almost certainly check in at twice the weight of the smaller Satoh. What that means, in my applications, is that there is significant disparity in what the tractors will do in terms of ground-engaging, but not really any difference in terms of mowing, running a tiller, or something dependent upon PTO horsepower.
The 186D will stall before it spins in most conditions except unusual attitudes or very soft soils. The Satoh (or my comparable Yanmar 1401D) will virtually never stall, and will excavate holes with the tires until it rests on the belly pan.
The 186D, given its beefiness and extra weight, would be much better with a loader than my 1401D is, and pulls a disk, plow, or box blade extremely well. The Powershift transmission is a real productivity booster for back and forth work or where you need to adjust speeds (Frequently while mowing, since it's kind of underpowered for what it will otherwise handle). For snowblowing, tilling, general gardening work, mowing, or other general purpose work the lighter tractors don't really give up much.
As far as things to check, the generic things apply: Overall condition, owner knowledge/maintenance history, and the like are a given. Specific to the machine, everybody who has one says the 186Ds have a strong and fast hydraulic lift. Whatever implement the owner has on back should move up with authority. If it doesn't, then the front should be lifting instead. Seriously. One end or the other will be coming up. Everyone also comments that it tends to lower the three point hitch rapidly, too. As in, be nowhere near it when attempting to inch it down, because it's going to drop like a rock.
The Powershift has, because of its design, a slight lag when engaging from neutral into a drive gear. It is similar to having an automatic automobile in park, with the engine idling slowly, then dropping it into gear. There is a perceptible lag, not an instant engagement. Once moving with the engine at rated RPM, shifts are nearly instantaneous, and feel like a musclecar with a shift kit in the transmission. Upshifts are certainly firm, and some might characterize them as harsh, especially if heavily loaded.
My 186D has a somewhat peaky powerband. I think it's normal, based on others' comments. It feels very weak until high RPM, where the engine is strong, but if lugged any, power quickly falls off. This is why the Powershift is so useful, since one can instantly downshift to maintain engine RPM.
Otherwise, I don't know of any real "gotcha" traits peculiar to the 186 models. Just be aware of the quirks particular to the machine, and see if it appears to be a good unit.
As Clemson said, generally this vintage Yanmar is at the pinnacle, along with Kubota, of the extremely high-quality but simple Japanese machinery. These, like the FJ40 and similar Landcruisers and Hilux pickups are easy to work on and maintain, and require minimal attention even in the roughest of environments. All of these things are around 25 years old or more, many are 30 years old. They still work great, especially after some deferred maintenance issues are resolved.
Generally, any problems that arise are due to abuse, owner neglect, or similar things. Running a mower behind a tractor without a properly fitted air filter is going to shorten the engine life dramatically, whether it is a 2011 Kubota/John Deere or a 1917 Fordson F. Having said that, most owners of new equipment admit they doubt their recent purchase will be running in 30 years of sitting out under the trees in the weather.
As a guideline, avoid a tractor that looks (Or is described as) factory new, with shiny, fresh paint, clean decals, and the like. They are often rebuilds of dubious quality imported from Vietnam. Some of them (Like my 1401D and some other users' machines here) are superb, and are no trouble at all. Others have nightmarish tales (documented) of engines or front axles from entirely different models, sometimes having different numbers of cylinders or incorrectly matched gear ratios. Again, these are 20 to 30 year old pieces of equipment, so should look like it, but that doesn't mean neglected or abused.
California, you're one of the best guys on TBN but this is why the "Mitsubishi guy" i.e. me, has to troll the Yanmar forum......well, OK there's only about a tenth of the traffic in the Mitsubishi forum so I have to troll somewhere. Satohs are super dependable and almost all but the early oddball and maybe largest models are well supported machines. They made a BUNCH of those and the variations of that thing under the Satoh and Mitsubishi brands and the Beaver III was even the U.S. model. Parts are as abundant as about any of the old Japanese compacts. Nothing will ever match Yanmars support but I would never pass on a Beaver because of worry for parts( at least at this point in time). and as far as technical knowledge, as long as people like Bill Rodgers and Len Sheaffer are around they will have dealers that can help owners with any conceivable issue anyone would ever have.
