“Is there some way to ask TwitterKarma to look at a second account once you’ve input the details for one account?”
The simplest answer is to close your browser completely, and the next time Twitter Karma tries to access Twitter, it will prompt you to re-authenticate. Of course, that’s no fun–I’d hate to close my browser and lose all my tabs, so I looked for another way.
In the Twitter API, there’s a “verify_credentials” method that, coincidentally, seems to change the effective user of the browser session if authentication is successful. You would invoke it by navigating to an URL like this:
Replace the USERNAME and PASSWORD with your Twitter.com account information. You should get a plain page back that just says “Authorized.” After that, reload the Twitter Karma page and click the “Whack!” button again. It should now load your friends and followers for the other account.