How to encourage communication by email or IM?

But for things like instructions, changes to the schedule or pay related topics, I much rather have them in writing.

With regards to changes to the schedule or pay related topics, I'd suggest you send a summary of what was agreed upon to the instant messenger every time there is a phone conversation about one of those topics. Same thing if he sends an SMS, or emails you, summarize and consolidate those messages to the main communication channel you've chosen for the both of you.

Basically, you're more likely to successfully change your own behavior before you can change his.

I was thinking if he had written the instructions in an email it would have been easier for us.

Written instructions may be easier for the recipient, but they're definitely not easier for the person who writes them. There is usually lots of tacit knowledge that gets accidentally skipped during the writing process. And it takes a very diligent person and multiple passes to write good enough instructions that can be followed by anybody.

Instead of asking him to do all that extra work, since he's your boss, and since he doesn't have much free time anyway (since he keeps on getting interrupted), I'd suggest you start recording your screen (with his permission) when he shows you how to do something on your screen. There is lots of free software that allows you to do this. But first see if the builtin software you're already using doesn't already have such functionality.

Once you have the recording, then you can write down the instructions, take screenshots, and post the entire thing on an internal wiki or something.

Also depend on your boss only for the business-specific information you really need to learn from him. In other words, if some of the information you're missing is generic enough to apply to any business, try also asking Google or AI, or looking for related-tutorials on youtube.

You probably can't. If you're a part-time contractor and your boss owns the company, it's probably incumbent on you to adjust your working style to match his than to try to convince him to adjust his working style to match yours.

In this specific case, it's not at all clear that an email would have saved time. Sure, it may have saved you some time waiting for your boss to deal with whatever issues came up. But writing the email would almost certainly have taken your boss more time than meeting with you did. So your boss would have been pulled away on other things more than 2-3 times and would have to have jumped back into drafting the email. Plus, the likelihood is that had your boss put the instructions in an email, something would have been unclear and you would have had to have replied to the email asking for clarification which would then have required your boss to again pick up this process and figure out where his original email missed the mark. That takes time and context shifts for your boss. A meeting was likely the most efficient way for the company to transfer the knowledge from your boss's head to your head even if an email might have been more efficient for you.

Depending on how you were meeting, you might want to explore meeting software that allows you to record meetings and that produces text transcripts. Potentially, that frees you up from the need to try to take notes during the meeting and makes it easier for you to rewatch part of the discussion if you get stuck in the future.

I assume that you're working for a small business. Small business owners generally start hiring part-time help when they reach the point that they don't have enough time in the day for all the things that need to be done and they need to free up their time to focus on things only then can do. If that's the case, whatever your actual job description is, your actual job description is really "Save your boss time." You want to focus on things that save your boss time not necessarily things that save you time because your boss is already at the limit of the time he has available.

Phone calls are a synchronous medium. You get the call when I want to reach you, instantly. You use phone calls when you want instant communication. It is also the fastest communication unless one of us has to investigate something before they can reply.

E-mail is the most precise communication. It is asynchronous which means I can send an email when I don’t expect you to read it or reply instantly or when I expect that writing a reply will take long time. It leaves a trace, so we can both collect what was said. It is suitable for large amounts of information. It can be combined with a phone call - I can send you an email and call you if I want you to read it instantly.

Direct messages will be inferior to one of these methods.

Pick your communications method according to your needs for that message.

Since you're dealing with the boss all you can do is say something like: have you considered using xxxxx app? That way we have something I can refer back to and you won't be interupted to contact me.

It is BS (it is true in logic, but not in why you are saying it), but it might work.

UPDATE: Ironically my answer isn't communicating the point that I am trying to make. In retrospect, with this edit might get this across to the DV'ers.

1. Stop assuming the boss is an idiot.
2. Stop assuming the boss's world is the same as the OP's.
3. Stop assuming the reason to use a given app by a dev is obvious to the boss.

Then being specific as the why and benefits. It is much different than saying "let's use an IM".

There is a bad habit of many devs being a bit sanctimonious when interacting with others. Assuming/Expecting/Requiring that everyone thinks like them is first on that list. I am not saying that the OP is one of them. Some of the comments maybe.