How to easily access your Youtube Inbox! 2013
UPDATE: another easy way is to bookmark your "www.youtube.com/inbox" and put it on the browser's top bar and click it any time.
Youtube is so stupid since Google took over it, so I mainly moved to Archive.org, but anyway.
About the instant access to your youtube inbox. This works if:
1. You have two youtube accounts
2. If other youtube user sends you a private message.
As for now, every Private Message received is shown in the main page to the left in Messages bar. Go to your other youtube account and just send yourself a private message on your other account, and viceversa. But don't ever read your messages, so they will stay in your main page forever. Or at least until youtube comes with another stupid idea of changing layouts.
From there, you have instant acces to your youtube inbox anytime.