The sentence is intended to convey that it is easy to fall into a pattern, and the pattern might be one of two types: consecutive sentences or repeatedly introducing paragraphs in the same way.
It’s easy to fall into a pattern of using introductory phrases while writing either in consecutive sentences or at the start of multiple paragraphs.
It’s easy to fall into a pattern of using introductory phrases while writing, either in consecutive sentences or at the start of multiple paragraphs.
It’s easy to fall into a pattern of using introductory phrases, while writing, either in consecutive sentences or at the start of multiple paragraphs.
The first obeys the rules as I understand them, but I think it creates a trip hazard because the 'either' could plausibly be constraining 'while writing', and only the 'or' clarifies that it's talking about the pattern.
The third also obeys the rules as I understand them (setting-off a nonrestrictive clause with a pair of commas), but it does not match the original thought or spoken tempo.
The second matches the thought and tempo, but I cannot identify a grammatical rule that would justify the inclusion of the comma.
I have studied a number of comma guides before asking this question, including: https://www.iue.edu/student-success/coursework/commas.html https://www.grammarly.com/blog/comma/
EDIT: But I had not seen this one, which may contain the answer I was looking for: https://owl.purdue.edu/owl/general_writing/punctuation/commas/extended_rules_for_commas.html