The Verdict: Not eligible
There is no Japanese citizenship through a grandparent: it passes from a parent only. Look at our Diaspora & Religious Return route for Japan, which gives grandchildren a strong residence status.
The Nationality Act has no grandparent provision and no generational extension.
What Japan offers third-generation descendants is Long-Term Resident status: any job, renewable periods of up to five years, permanent residence after five years, and no Japanese-language test. Your parent must have been born as the child of a Japanese national.
Check your parent before you rule them out. A grandparent who emigrated but never naturalised elsewhere stayed Japanese, which would have made your parent Japanese at birth. If so, your parent may still be Japanese, and you may be too. Your grandparent's family register (koseki) settles it.