The method in the Noble Eightfold Path in right speech for persuasion and influence What does the Noble Eightfold Path say about right speech when it comes to persuasion and influence?
While persuading and influencing are not part of the standard definition of Right Speech, it certainly is considered inappropriate for monks and not part of Right Speech for monks, in the context of monetary gain or politics or other worldly endeavours not suited to the holy life, as seen below.
From DN 2:

&quot;Whereas some brahmans and contemplatives, living off food given in
faith, are addicted to running messages and errands for people such as
these — kings, ministers of state, noble warriors, brahmans,
householders, or youths [who say], 'Go here, go there, take this
there, fetch that here' — he abstains from running messages and
errands for people such as these. This, too, is part of his virtue.


&quot;Whereas some brahmans and contemplatives, living off food given in
faith, engage in scheming, persuading, hinting, belittling, and
pursuing gain with gain, he abstains from forms of scheming and
persuading [improper ways of trying to gain material support from
donors] such as these. This, too, is part of his virtue.