Pokemon-go – How to login if I never set a password

As far as I know (I don't have a source other than personal observations), Pokemon GO doesn't access your Google account at all.

When you "log in with Google", the game checks whether a Google account is present on the phone and what the associated e-mail address is, then loads the Pokemon GO account identified by this e-mail address, without ever trying to access or otherwise use the Google account. It has a completely seperate account based on your Google account's e-mail address, which is the only thing it needs to load that account, operating under the assumption that the Google account would only be present on the phone if you had the password.

Therefore, Pokemon GO will never show up as a connected app in your Google settings. You can't revoke access because all it ever needs is the name of the Google account linked to the device and you really can't hide that from an app. (Also why would you?)

This also means that should Niantic ever shut down their servers, everything Pokemon GO related will be gone, there will be no way to get any records pulled out from your Google account. If someone subsequently created a fanmade clone of Pokemon GO, everyone would have to start over from scratch, it would be impossible to pull any account info from Google or Trainer Club because there's nothing there. This is notably different with games that actually connect to Google, those store settings and usually progress in the Google account and if they discontinue the service, someone can just take over.

Try using a password that is between 6-15 characters in length.

I was able to sign up and sign into the PTC website with a password that is greater than 15 characters in length, but my password was incorrect according to the PG application.

My next move was to sign into the PTC website and attempt to change my password from my account settings page, however the input fields indicated that my chosen password was invalid because it was greater than 15 characters in length.

Finally, I changed my password to something within the character limit and I was able to immediately log into the PG application.