Moving on to one of those heroes that I'm not very good with it, but like to play nevertheless. Brewmaster has some of the best quotes in the game - so, at least you can listen to them while failing as a support.
My prediction for support Brewmaster was not that strong, primarily because he needs to be in melee range to be useful, and he has some serious mana pool issues. In theory his ultimate is just as strong without farm as it is with farm. However, he generally farms items that allow him to get his ultimate off more effectively - items like Blink Dagger or in some cases Black King Bar. Another reason why Brew is played as a core has also a lot to do with his ultimate. If he gets to level 6 early, he can dominate early game fights in a very convincing fashion. Supports' levels are often delayed compared to those of cores, unless you are fanatically leeching experience from a safe lane carry. Jungling supports can also get quite fast levels, but unfortunately Brew doesn't have a suitable skillset for that. In other words, you will be playing a melee lane support who has no stuns.
So what does he have? Well, his first skill Thunderclap is an aoe nuke and a slow and an attack slow - but it only hits around Brew, requiring him to be in melee range. His second skill has higher utility since at least it's ranged. The miss chance can be useful in the same way as Bane's Enfeeblement, to deny last hits from an enemy carry. However you need a substantial amount of mana regen to spam it. The slow is useful for chasing, allowing you to catch up and use Thunderclap. His passive is not all that effective for a support. It's kind of useful if you are facing a melee hero, as it allows you to trade hits more favorably. Most of Brew's effectiveness will still come out of his ultimate Primal Split, which gives a staggering amount of teamfight control and damage, especially in the early mid game. As a support you'll have to rely on walk-in ults at the time the skill itself is at its strongest. Obviously this is not very effective.
I think maxing Thunderclap first is still the way to go. Grabbing that one value point of Drunken Brawler should also be helpful, but beyond that you might want to max Drunken Haze second even though its scaling isn't that hot. That 75% miss chance at level 4 is still going to be very annoying for enemy carries to deal with, especially if they don't otherwise want to build either of the bars. The ranged slow is also going to be helpful whenever your ultimate isn't up - as a support you should expect to be fighting quite a bit more without it.
I don't think there's much reason to deviate from the standard Brew build. Just go for that blink, even though its timing won't be very good unless you're somehow racking up kills. Getting an Orb of Venom after boots could be a good idea to improve your chasing potential. Buying wards is fine to some extent, and thanks to your ultimate carrying a gem is a lot safer than it would be on many other supports. Of course as a melee hero you need to bring a Quelling Blade to actually deward cliffs. If at all possible, just try and save for that blink. Grabbing arcanes at some point should be beneficial. If it's hard to get a blink, going arcanes first at least allows you to get more out of your other spells and still have mana for Primal Split. Beyond blink, just get whatever seems the most useful and attainable. Vlad is a good option with lots of utility as is Force Staff (even more mobility!) You could also build for a Hex, but actually getting there might be difficult. Other useful options include aghs and refresher, to get more out of your ultimate.
Well, this here is the hard part. Brew is a rather useless lane support, and his ability to set up kills is nonexistent. If there is another support on your lane, or your carry can initiate, then Thunderclap is a decent followup nuke and slow. The same goes for ganking other lanes. You always need someone else to initiate - the best you can do is help them a bit with Drunken Haze. With 800 range you have a good chance of getting it off before the enemy realizes they're getting ganked, at least if you're smoked or it's night time. It might be possible to roam with, say, level 2 or 3 Brew this way, especially if you get that Orb of Venom. He's pretty bad at protecting a carry, and equally bad at harassing enemies or getting kills on a lane. So roaming is probably what you should do after leeching that second level either from the lane or from pulling. Beyond that it's all about getting those kills.
After finally getting to level 6, you'll be playing mostly like you would as a core who had his farm shut down hard. Because you have to rely on walking in to deliver your ultimate, you're very susceptible to silences and stuns. Two of the brewling are quite fast however, so you could just cast split a bit further away and then initiate with the water panda from invis. This does waste precious seconds, but it's better than dying without getting a split off. Using your ult to counter-initiate is another good way to get a lot of utility out of it. Just use it as soon as the enemy jumps in to screw up their plans. You should obviously avoid being the one in the receiving end of their initiation however.
Based on one bot match, I feel like I was mostly right. Although his ultimate in itself is the same whether he is support or core, it is indeed slightly harder to deliver. There is however another factor involved in making him a less desirable support: it's generally ok for cores to rely on a long cooldown ultimate to be effective as they can farm while it's down; in the case of supports, they generally are required to be active even while their ultimate is on cooldown. It is these in-between periods where Brewmaster is very weak compared to other melee supports like Earthshaker or Treant Protector. While his two spells have a certain degree of utility, they are inferior to true support abilities. In particular, the only thing he can do from any sort of range is Drunken Haze, and while the slow is nice and the miss chance is significant, they don't do all that much to turn a fight around.
Having to walk in to use your only nuke really hurts, and it's only a slow. This puts Brew into rather significant danger and you typically can't ever use Thunderclap if you also want to use your ultimate. Another huge problem is his abysmal mana pool. A lot of time is wasted going back to base. In situations where the slow from Drunken Haze is enough of a gap closer, he can gank pretty effectively. If you manage to land a Thunderclap followed by a couple of poison attacks, most enemies should not be able to get away. However, Drunken Haze is not the best gap closer and generally requires a smoke in daytime to get close enough from a suitable angle. His burst damage is also quite weak with just one 300 damage nuke and a guaranteed double damage crit.
Support Brew is therefore a bit too greedy. While he can theoretically be very effective in teamfights, the in-between will be tough. His levels are also very likely to be late compared to a core Brew, and even more so his blink. I stand by my initial judgement, placing him in the poor category.