I'm aware of only one fish eye dish in Japan, namely maguro no medama-ni (マグロの目玉煮), "stewed tuna eyeballs". It's occasionally branded as the more palatable "マグロのDHA煮" after DHA, a fatty acid found in eyeballs and fish oil that's supposedly good for you. Like the name says, this consist of tuna eyeballs (which are pretty big!) stewed for hours on end in the usual Japanese soy-mirin-sake-dashi base until they more or less completely fall apart into mush, as shown in this picture (not CC so I can't copy it in, alas). Incidentally, the pupils and eye sockets stay hard, you only eat the stuff in the middle.
This is not an everyday item by any means and it falls squarely into the category of chinmi ("rare tastes"), meaning odd foods/acquired tastes meant primarily as accompaniment for drinks, and the kind of thing that makes an occasional appearance in the daily specials, not a fixture of the regular menu. A search on restaurant review site Tabelog reveals 15 hits in the entire country, all in reviews where people claim to have eaten this. The only place I could find (and I didn't look all that hard, mind you) that has this on their website menu is a tuna specialist called Hanamaguro (花まぐろ), rather inconveniently located in Kochi city on the southern coast of the island of Shikoku, whose まぐろ漁師の賄いもん 目玉の煮付け ("Tuna-fisher's catering item, eyeball stew") will set you back ¥680. Itadakimasu!