Sake. How is sake akin to a fountain pen?

Both
in the pursuit of pleasure -- poetry & libation.

But let's begin with definition. Do I mean sake the drink? Or sake the Japanese salmon which I have enjoyed for dinner & lunch recently.

Both.

& the pleasure of writing with a fountain pen while remembering the taste of sake.

Both.

Sake. Why is sake perfect to accompany the short poem?

Culturally it infused the Japanese short form as well as the poet. It offers clarity and then develops into a soothing fog.

It translates mighty well to the American ku.

And if your mind isn't turned to poetry, sake does sashimi proud. By the way, sake, sashimi and poetry are wasabi friendly.