I used to help run a yakitori pop up. At home I have a setup on top of an old grill made of fire bricks and heavy foil and some steel tube/bar stock to rest skewers on. Works equally fine as our purpose built grill we imported back then. Happy to answer questions and will provide more thoughts later.
More thoughts!
Yakitori is a really fun style of cooking, there's an infinite amount to learn but at its core it's also really quite simple, it's incredibly prep heavy, it's hard to do without volume of birds/customers/etc., it's hard to get better without repetition, quality of your bird is really important (bad won't work, great is best, good is still fine), and it's a really hard one to pull off for any home based group (people wanting to eat all at once in the western traditional dinner party sense).
Gear - I use a fire brick and aluminum foil with steel stock and simple mesh restaurant grates setup that works great for me. It sits on an old charbroiler from a restaurant in my yard so it gets great airflow from below, very little from the sides. I imagine you can make something similar with any old brick on a grill and be in it for a few bucks if you want to try it out. We had a big grill for the shop, akin to what you'd see in japan (I think this was pre konro being that prevalent so we imported it.) We ended up really liking L-shaped metal for the bars vs. the hollow tube stock it came with. They seemed to block the long ends of the grill, focusing the heat to the center which meant less charring/heat on the part you grab and turn. I found we got singed ends and sometimes breakage if there was a gap between the grill wall and the bars if that makes sense. That's the main piece of gear besides what you keep tare in, the skewers used, etc. Flat skewers are a must, anything else will spin. I think ours were from mtc or trueworld but there's so many options now. We used a hand fan for coals and metal grates for things that needed it and that was kind of it.
Binchotan - We used it exclusively, several different kinds. We had tough luck with Thaan but I like it for other stuff. Our main issue was fat tended to flare vs vaporize (seems like woo woo but it's noticeable. Not all the time, flare ups still happen but it does make a difference). When starting binchotan, wear safety glasses, it can pop violently as it heats up. We started it in a chimney starter on a wok burner for a shocking amount of time. We dunked ours at the end of service in water and re-used it for several services. We set up a hot area and a less hot area in the grill (mostly full and partially full.) If we needed more mid service, we found it was best to start it fresh vs. load fresh onto the grill (our grill was small and this kinda messed with temps, plus the popping)
Chicken! - Ours was from a local farm. They did enough where they processed and saved organ meats for us as they ran through a lot more processed birds than whole birds and were left with a lot of misc. (Mostly gizzard, breast bone, skin, hearts, liver.) Besides that, we processed whole birds and saved up stuff and rant it as specials when we had the quantity we needed (pope's nose, that flappy meat near the rib cavity, knee cartilage, etc.) Tsukune recipe testing was extensive. It's kind of the savior of the whole process. You get to grind a lot of the misc. (breast mostly) and turn it into something more exciting.
Labor/prep - It's immense. Ironically, skewering took more time than butchery. It was crazy laborious. Break down 10+ birds a day into very specific component parts, then into skewerable pieces, grind chicken for tsukune and form that, make more tare (carcasses and bones went there), veg prep, etc. The skewering take so much time because getting the hang of manipulating something that isn't intuitive (I want this amorphous chunk of thigh to sit like a consistent rectangle so I skewer it like I'm folding a fitted sheet) takes a lot of practice. Thankfully, you can mess it up and it's still tasty, it's just not as good as it can be and it can really mess up workflow trying to cook irregular pieces. Consistency of size is important along the skewer because it very much impacts how it cooks. If you have a fat end and a skinny end, you're going to flip it a lot or put it on a rack and it's going to mess up workflow. After a while, you get a sense of how hot your grill is where, and what size pieces and what position on the grill is best for different cuts. Prep works best in groups frankly. There were typically 3-4 of us doing prep through service (some grilled, some switched to FOH). I'd dislike doing it any other way at scale. Veg was half the fun as well!
Cooking - Not much to say, it's an attentive cooking process, it's hot, you figure out how the grill is going as you cook on it. Eventually it makes sense but it's a little different each day when you load it. You will likely make your pieces too big to start. Your prep determines how easy or hard your process is.
Seasoning - Usually salt or tare. There's a lot of playing you can do beyond that but those are the main things. There isn't a ton of room to hide. It's well skewered, well seasoned, well cooked meat, and the components should match each other (like for me sasami was always a salt thing, never tare, which we ran sometimes usually with wasabi or ume paste or a shiso salt. When you try enough you'll find what makes sense for you and your tastes.)
Eating! - We ran service with some cold dishes to share and pick at and a big drink menu. This is a drinking food more than a meal. Potato salad, pickles, aemono, other items picked up from the sister restaurant, etc. That way, skewers can come out as they come and no one on either end is stressing about it. At home, we typically just do the same but clustered near the grill. Homestyle in japan is the same way, which is why you see a ton of table top grills around (and prepped yakitori that people takeaway and reheat at home.) Doing it for others vs. with others leads to just an awkward style of eating/entertaining so it's hard to see how it translates unless people are more willing to move in a different way than they're used to.
Chicken and charcoal is a good english language based book
I've found this book to be really useful.
https://www.amazon.com/やきとり_11店の技術と串バリエーション-Shibata-Shoten/dp/4388060380