You cannot sell the gains. You can only sell your investments. If you are selling them for more than you bought them for, you pay capital gains tax on any gain.
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I understand -- I am not selling "gains", I am selling shares. And it's the difference in value of those shares from the purchase price to the current valuation that I am paying capital gains tax on.
I think one of the reasons why I am so confused is because Monex (as well as other institutions) allows you to input the Yen amount of what you wish to sell, and the backend will automatically calculate the number of shares to facilitate that. Also, in the Monex investment display, it shows how much a particular investment has appreciated/depreciated since the day before (for mutual funds) in Yen. I think these points are part of why my mind is always thinking about these investments in Yen.