Go to your Evercontact for Outlook Personal Page:

 

 

Click on the "Change to" tab and then click the "Switch to Evercontact for Gmail" button.

 

Uninstall the Evercontact for Outlook add-in via the Windows Control panel: 

 

Then click "It's uninstalled!" in the pop-up on your Personal Page:

 

 

Give Evercontact authorization to securely access your Gmail account by clicking "Continue" :

 

Click "Allow" to give Evercontact the necessary permissions, and then (if prompted) sign into the email account you want to switch to Gmail.
 

You're account will then be switched to Gmail, and you will be taken to your Evercontact for Gmail dashboard for the first time.