Japanese b2b: email tips and proper ettiquette

I'm a USA client who buys inventory from a Japanese b2b supplier.

I come from an Asian American household, but I have lost touch with my heritage since I just lived in USA my wholelife (I can only speak English), so I'm probably oblivious when it comes to proper ettiqutte/manners from the country my parents emigrated from.

I communicate mainly via email with the person handling my account, and even though she is almost fluent in English, some things are awkwardly written or even slightly mistranslated. Overall, I'm happy because she can actually talk and speak English, and is part of the international sales team. Other suppliers I have dealt with did not speak any English, and I would do my best to properly interpret and also translate whatever that needs to be communicated (I mainly use DeepL for my Japanese translations, but I always see sentences change a lot when i convert from Eng -> Japanese -> English -> Japanese), so this is a breath of fresh air.

How can I go about building better international business relations with someone that I exlusively (so far, but a phone call is possible in the future) communicate with via email? Are there certain ettiquettes that I should be aware of? I know with some USA-USA businesses, what starts off as formal can lean into a little more informal and friendly as the business relationship grows. Are there any tips or ideas on what I can do to make the business relationship stronger? At the moment, products are often allocated and distributed according to their descretion. Because I am a new account, I'm likely an account that does not get allocated any inventory or very little inventory if at all. Right now, I am just looking for proper ettiqutte and tips to build a strong, healthy relationship with the other business, and if there are things I should be actively doing and not doing (like is it okay to email on weekends? should i ever send a gift on holidays? etc).

Any advice would be greatly appreciated

Formal is good. Formal shows respect. Formal shows professionalism. As an American, we tend to think that everyone wants to be friendly and wants to do away with formalities and break down unseen barriers between people, but in Japan this kind of familiarity is just awkward. Don't worry about making friends with your contact...a solid business relationship doesn't need to be casual or super friendly.
Cordial and formal, or cordial and "relaxed formal" as you become more comfortable with each other is a good thing. Be punctual, acknowledge mails or shipments, do everything you can to make the other party's job easier, obviously pay on time. Take responsibility - don't say "sorry I didn't respond sooner, my car broke down" or whatever the excuse is. Japanese companies don't want to hear the excuse. They just want you to take responsibility. "Sorry I didn't respond sooner. I apologize for the inconvenience I caused" is the correct response.
Emailing on weekends is fine (but don't expect a response). If you do get a response, you can say, "thank you for responding so quickly" (recognizing their extra effort).
I don't know how you address your partner, or if they have indicated some preference for how you should address them, but here formality is also obviously good. Mr/Mrs Familyname, unless otherwise advised.
All basic stuff, I guess, but Americans sometimes find it hard to suppress the urge to be casual/funny/jokey, because they find formality somewhat cold and awkward, i guess, but in Japan "formal" is preferred, unless you have a genuine close relationship (but even here, business correspondence tends to be formal).
Sending gifts? This is a tough one. In Japan, some gift-giving used to be standard among partner companies - especially at New Year's and mid-summer. Nowadays, companies are refraining from this more and more, partly for cost-cutting, and partly because the custom can be problematic from a compliance point of view. But old fashioned companies still exchange gifts - and department stores package up items especially for gift-giving: boxes of crackers or biscuits or canned juice, etc. As a foreign company I wouldn't spend too much time wondering whether I should send a gift. Sending it and getting it through customs might be more trouble than its worth AND it might make your partner feel obligated to reciprocate. So, my advice would be to not worry about gifts. Being aware of Japanese holidays, on the other hand, would be good. "Dear Mr/Mrs Suzuki, I hope you enjoyed your Golden Week holidays. ...". But that is about as far as I would go.

Appreciate your thoughtful response.

I noticed I may have sounded like I was trying to steer my rapport with the person in a unprofessional way, but I really just meant talking more businesss casual rather than informal. So far, our correspondence has been, "Dear <name>," and X, Y, Z questions/answers.

I actually already do the basic stuff such as "I hope you had a great weekend." and "I appreciate your time and patience answering any questions I may have" etc.

Is it improper to eventually want to form a business relationship where I can just say, "Hi <name>, how was your weekend? I was finally able to eat at this restaurant that I have been meaning to visit for some time now (or some other example)." and then get on with the main purpose of the email, or is even engaging in small talk entering "too personal" territory? I'd like to think that we're all regular human beings, and connections grow stronger when we are fairly comfortable with each other. I guess im just wondering is if it would be okay to engage in some light, brief small talk or if that would be considered inappropriate or off putting.

xedwin said:

Appreciate your thoughtful response.

I noticed I may have sounded like I was trying to steer my rapport with the person in a unprofessional way, but I really just meant talking more businesss casual rather than informal. So far, our correspondence has been, "Dear <name>," and X, Y, Z questions/answers.

I actually already do the basic stuff such as "I hope you had a great weekend." and "I appreciate your time and patience answering any questions I may have" etc.

Is it improper to eventually want to form a business relationship where I can just say, "Hi <name>, how was your weekend? I was finally able to eat at this restaurant that I have been meaning to visit for some time now (or some other example)." and then get on with the main purpose of the email, or is even engaging in small talk entering "too personal" territory? I'd like to think that we're all regular human beings, and connections grow stronger when we are fairly comfortable with each other. I guess im just wondering is if it would be okay to engage in some light, brief small talk or if that would be considered inappropriate or off putting.

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As s Majestic said, it could be odd or offputting. I think it depends on the person. I suppose you could try something like "I heard in the news about the heat wave, I hope it's not too bad for you." Or "I heard about the recent earthquake, are you ok?" And see if they respond in kind. If they never respond except to answer your questions I'd probably keep the small talk to a minimum.
Note: don't try these particular ideas until there's actually a heat wave or earthquake.

xedwin said:

I'd like to think that we're all regular human beings, and connections grow stronger when we are fairly comfortable with each other. I guess im just wondering is if it would be okay to engage in some light, brief small talk or if that would be considered inappropriate or off putting.

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This is precisely the kind of thing that you should avoid. I know we like to think there is a commonality among people, but revealing these even minor personal details should be avoided. If your counterpart has spent time in the States and initiates some casual conversation, it might be OK. But the urge for you to break down perceived barriers by chatting about what you do/did in your "off" time is usually awkward for the receiving end. Why? Because formality has a certain value in Japan. When you start to insert yourself into the correspondence, you are, in a way, showing that you don't respect that value.

If you become good friends with your counterpart, which could happen in Japan, you can introduce some familiarity into the correspondence, but (at the risk of repeating myself) business communication tends to favor the formal rather than the casual.