Dear Sir/Madam,
Based on the description you have provided here I can definitely help you with your implementation. While i don't have experience specifically with the Gmail API (i had a quick look) it is extremely to similar to other Google APIs e.g. Youtube, Calendar, also Spotify (not Google) etc. All of which are APIs requiring OAuth2 and I have experiencing implementing, login -> get token/refresh token if needed -> call api.
I do have one question, are you looking for just the OAuth2 part to be implemented (i.e. all the steps besides implementation of any specific api e.g. fetching your emails or a certain email). If you have any questions or doubts please feel free to contact me, I would be happy to help and do looking forward to hearing back from you soon to discuss it further.