Fix Gmail Integration Issues

I need assistance to fix the Gmail integration in our internal company webapp. Currently, we are facing authentication issues, specifically login failures.

Key Requirements:
- Fix existing Gmail integration issues by updating gmail integration method
- Resolve authentication problems, especially login failures
- Take appropriate backup of code and all configuration to restore if there is a need to revert the update

Ideal Skills and Experience:
- Experience with Gmail API
- Strong understanding of OAuth and authentication protocols
- Background in web app development and debugging

Please provide a detailed approach and estimated timeline.