SD Twitch Stream can publish or unpublish modules and menu-items based on the online presence of a streamer. This way your website only shows online streamers! Combine this functionality with the Random Module Module to show a random, but currently online streamer.
Enabling the feature
Enable the option to publish or unpublish the menu-item of module based on the selected streamers' online presence on Twitch.
You'll need a running and authorised cronjob for the feature to work.