You have a lot of different options for saving your Gmail messages to Evernote, but most of them require that you give a third-party access to your Google account. That should be fine enough, but if you'd prefer not to do that, Digital Inspiration shows you how to roll your own forwarding service.
Digital Inspiration uses a Google Sheet that creates a script where any messages in your Gmail account with the label "Evernote" get forwarded to Evernote. It's simple, doesn't require any external services, and it's easy to set up. Head over to Digital Inspiration for the full guide.
Quickly Save Your Gmail Messages in Evernote with a Google Sheet [Digital Inspiration]