How do I get around HttpError 403 Insufficient Permission? (gmail api, python)
Even though the accepted answer is 100% correct. I think it's worth pointing out that why that's the case.
When you authorize a gmail service client, you can specify several different scopes: All, compose, labels, etc...
These are all listed here: https://developers.google.com/gmail/api/auth/scopes
The scope mentioned in the answer provides complete gmail access.
Gmail API has these scopes: 
For sending emails, https://www.googleapis.com/auth/gmail.send is needed or full access https://mail.google.com/.
The scopes taken from here.