On a plane, was written : “Fasten your seat belt while seated.” What is the grammatical rule of “while seated”?


I don’t fully understand what you mean by a grammatical rule. This sentence is short for Fasten your seat belt while you are seated. Signs and headlines often use a style, called block language, that excludes pronouns, the verb be, articles, etc. You can read about block language and about abbreviated sentences in instructional writing in Quirk et al, A Comprehensive Grammar of the English Language, pp 845-848.
:friendsxs3:

The book written about Besho is useful.
Use :which