On my Mac I use Safari and am logged into multiple gmail accounts at the same time. I tried out the Mailbird integration last night, and was pleasantly surprised that when accessed via the browser it actually attempts to launch gmail. Unfortunately, it always tries to load the email in the first account. I knew that specifying the account must be possible, because other apps I've tried were able to do it. Here's the only change that is needed:

The current URL launched is, for example, https://mail.google.com/mail/#inbox/MESSAGEID

If you can pass the email address of the account the message belongs to, gmail will select the correct account before loading the message:

https://mail.google.com/mail/?authuser=EMAILADDRESS#inbox/MESSAGEID

Please see if this change is possible in the existing Mailbird plugin and additionally please see if you can make sure this is done when the gmail integration is complete -- it would help those of us with multiple gmail accounts immensely.