If it is a small Yakitori restaurant called Umemitsu (梅美津) in Shinbashi, it is actually patrons/reservation only.

There are quite a few patrons only restaurants in Tokyo.

And there is a word for it in Japanese " 一見さんお断り" which literally means "does not serve first time customers".
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That phrase is often used by relatively small, old Japanese style looking restaurants run by one chef or two.
Those places usually accept patrons or someone with patrons.

For those restaurants, it does not matter if you are Japanese or not.
And usually you don't see any signs stating it is patrons only even in Japanese.
So it is hard to tell which one is patron only or not unless you can read Japanese and search online info.
And if Japanese try to go those places not knowing it, they will just say "does not serve first time customers" in Japanese.