I went ahead and added my work account to my personal account's chrome session and then revisited the google auth link from my main SO account, and this time it gave me the 2 options, and I successfully added it. However, I don't think it should work this way! You should get that screen that either allows you to select an existing logged-in account, or add a new one.
@RudyOnRails Yeah, I agree. Looks like there's a parameter we can pass along for that, though I'm not sure off the top of my head how much work it'd be for us to start doing that for the "add login" path. Could you do me a favor and write up a quick feature-request for this so we can track it easier? Thanks! – Adam Lear♦ 20 hours ago