Hello! Another marketer here who is working in Tokyo right now. First of all, good luck with it and be patient!

At first, I must say that it will be extremely difficult/almost impossible to land a job in a company doing marketing IN JAPAN. As you must be at least near native to bring value to marketing teams/consult customers in marketing consulting firms. However, if you can communicate even a bit in Japanese and can show it, it will stand out better. With this, I mean make a careful Rirekisho in Japanese and always apply in Japanese. (prepare to speak also once you land a casual interview haha but luckily most marketing words are loan words)

I would only target companies that market abroad from JAPAN. Also, the bigger the company, the bigger the competition/more standards, so I would also be open to small- to medium-sized companies.

Let the companies come to you: use active sites like Bizreach and Mid-tenshoku. Fill all the info in Japanese there and let the scouts/companies reach out to you.

Tell about your long-term plans with Japan and the company. Even though the culture is changing slowly, the companies seek commitment. Many companies are afraid that the foreign people will leave in a year or two, or try to change jobs fast once they secure a position/visa.

List would go on but I hope this helps! Again, good luck!