I've been recently getting a lot of inquiries for random classic/vintage car parts to be bought from Japan.

The thing to remember folks, is that for anyone in bigger cities in Japan, it is very different for people in Japan.

It's one thing, if the shop has it and is willing to deal in English language and takes payments from foreigners, and wants to ship. But for most cases, these guys are older, and is content with doing business locally, and for many are reluctant to deal with foreigners. We can't blame them as Japanese culture and community is very uniform and safe. A lot of foreign transactions from many countries are thought to be unsafe, and people are not willing to deal with it. Period. Also, because they have plenty of demand within Japan, they are not really eager to start anything out of the ordinary, though anyone looking in from the outside feel they should. It doesn't phase them though...

Secondly, for folks in Japan's cities can't just hop in a car, drive somewhere, and fetch something, and return home like many of us Americans. Their gas prices are more than twice the US prices, and highway tolls are few bucks every few miles, and parking prices can also be as much as what you'd pay in Manhattan. For many, it often takes a few train trips and a lot of walking too. They are hard working people who have much less time in the day from their daily chores and work too. When they pick up large pieces, they have very little room to store anything for long periods between shipping too.  So having a third party or a friend do a favor of buying and shipping something is also something a bit more involved than most of us in the USA.

Lastly, for many of these shops the foreign transactions are something secondary. You see in Japan car parts shopping is done almost strictly by shop owners and repair/restore industry personnel and not generally by hobbyists or owners from public domains. So not only are they accustomed to public inquiries, but also aren't in need of setting up vast catalogs for public viewing on the internet either.

So having said all this, it isn't like they don't want to sell you stuff. It's just that we need to take these things into consideration, and be considerate and patient, and willing to spare then extra fees and expenses too. If you are prepared and thoughtful of how things are in Japan, you can avoid issues, and frustrations and deal with importers and dealers in Japan too, smoothly. You may also consider buying from a reputable shops online like Bend Brothers for a hassle-free process.

Take note of these if you're buying random collectibles from Japan, not just car parts but most other rarities as well from anime goods, art, and trinkets to tools. Good hunting!

PS:  If you have large items to ship, consider talking to a expert importer who can arrange logistics and payments that are easier BEFORE YOU leave.  That way you have a place to ship to in Japan and whoever you buy from can ship them directly to that agent where he will ship them for you, so you don't need to carry it around trains in Japan during your trip either.
KJ Takahashi of MyJapanDirect is such a guy, and he can make arrangements like this, or even hunt and order things for you without you having to leave Japan!  https://myjapandirect.com/