A channel that plays music videos from a playlist. Non-stop. The way to accomplish this has changed a bit between 1.0.x and 1.1.x

• Get the music videos you want to play.
• Save them in Plex. A common way to store Music Videos in Plex is to create an "Other videos" library. This way you won't have to worry about naming the videos in a specific way to match some agent's rules. But there are many other ideas and options. Some people use music libraries, which apparently support videos as well. You may also prefer to use a separate "TV" library and create fake TV shows for the artists/albums.
• Add the music videos you want to some plex playlist.

Stable (1.0.x)

In the stable version, what you want to do is create a channel. When the channel is empty, there's a button that allows you to 'schedule Flex time'.

"Flex Time" has many issues, normally we use it for 'commercials'. But overally it is just a time segment where random videos are played. The random videos are specified on a per-channel-basis. in this case, you want a channel whose unique programming is Flex time. Pick 3 hours or so of flex time and add them to channel.

Then click the Flex time in the schedule, in the new view you can add video clips as filler for the Flex time. This time the fillers you want are the music videos from the playlist you saved in Plex.

Edge Versions (1.1.x or greater)

The Edge Version works similar, but there's an additional step. You first need to create the filler list. In the top navigation menu there is a link called "Filler". This is where you can create a filler list where you'll add the videos from the Plex playlist.

Then, when creating the channel and after adding Flex time, click in the Flex time. There will be an option to add a filler list. Pick the filler list you just created.

There's additional flexibility now, you can combine multiple lists and tweak the random chance that a video in each individual list will be played.