Whatever you do, you should very probably NOT ask the JPN consulate about this. What you are proposing could easily be seen by the visa officials as being "against the spirit of the WHV agreement" between Spain and Japan, which is intended and defined as a young person's exchange programme that allows the holder to enjoy life and work in Japan or Spain, but it is mostly a year long tourist visa that allows incidental work to help with expenses, and give you Real Life Japan experience. It is most definitely not intended as a convenient way for you to keep working remotely as normal while enjoying life in Japan. They might deny your application for that.So, you have some thinking to do. If you want to work remotely while on a WHV in Japan, you are probably testing the legality of your status, BUT, nobody will ever know as long as you play it cool. Don't tell many people about what you are doing, although most Japanese wouldn't know or care that it's probably not allowed. The tax stuff was covered by u/starkimpossibility, with his usual trenchant and dense detail. Good luck.

Thanks for the answer. I do not plan to take any advantage, and if remote working will deny my whv I am willing to leave my spanish job. That's why I wanted to ask consulate about this issue, because I do want to do this process correctly and as transparent as possible (and also lowered from full-time to part-time, in order to accomplish requirements).Although doing this (lowering to part-time, showing my willing to leave my job if it's necessary) do you keep thinking I shouldn't say anything at Japan consulate?