GMail allows applications to connect in 3 different ways. Note: I'm working on some videos to take you through all these scenarios

The recommended option for eNotify is to use password-less authentication. You can use this form of authentication as long as your email account is managed by the Android device.

To use an App Specific Password:

To use your Primary UserName and Password:

Is the password-less authentication as reliable as the primary User Name and password?

Honestly, I don't know. It involves another layer of technology and managing access tokens. Also, you may need to periodically re-grant permission to eNotify if its permission gets turned off. For example, if you access your account from eNotify in 2 different countries that could in theory trigger an automated removal of eNotify's permission. I'm just guessing that individual apps will get disabled more frequently than your primary account. So if reliability is your utmost concern you may want to persist with User Name and password for now.

Why does GMail have so many different types of authentication?:

It is due to how Google accounts have evolved. Traditionally, we only used our primary user name and password for all apps. Google then added app specific passwords via 2 step authentication. Firstly, so that 3rd party apps don't need to know your password. But it also reflects the fact that our logins unlock much more than our GMails these days. While it was a good idea in theory, I think a lot of people rightly found it confusing not least of all because no one can explain what '2 step authentication' has to do with 'App Specific Passwords'?!?. The naming and concepts are not user friendly. With Password-less authentication eNotify simply sends a special Google token to the GMail server that asks you to grant eNotify permission to access your email account.

eNotify will continue to support 'User Name' and 'Password' authentication since it is the only option for most IMAP and POP3 accounts.