RetireJapan

Just double checking. If I sell something in my tokutei account all the tax is taken care of by SBI, right? Does that mean I don't need to do anything at all with regard to declaring it on a tax return etc? Just sell and be done with it?

Yes, but figuring out how much tax they'll take is a bit awkward

https://retirewiki.jp/wiki/SBI_Securities

There is an account type that does not do tax withholding on capital gains, but chances are you would have selected the tax withholding option.
源泉徴収あり is the type that takes care for you, 源泉徴収なし you need to report the taxes yourself.

Thanks @sutebayashi and @adamu - very helpful. Yes, it's the 源泉徴収あり type.