Character Animator Switch Scenes ?

So there are "scenes" in Character Animator where you can add different puppets and backgrounds etc to each scene. You can then export each scene individually (e.g. as a MP4 file) and join them together using Adobe Premier Pro, or now Adobe Rush (looks easier for simple Video editing like this).

But I think you mean "scene" from the acting sense. If you want a character say to walk across the screen or stand there and the background to change with the character puppet to not move, then you need to use one Character Animator scene and change the background image - which I think is what you are describing.

The main reason for me to start a new CH scene is to keep scenes from getting too large and complex - they get hard to manage.

So, back to your question, the "eye" hides that track - you cannot record it in a track. But there are two other things you can do to achieve what you are after. Background images are puppets. By default puppets get a set of properties, one of which is Transform. One of the properties of Transform is opacity. So if you load up two background images as puppets, then record a new opacity value for the image in front half way though you can make it disappear, revealing the background behind it. You can even do a "blend" to fade the opacity causing a "cross disolve" effect. That allows the puppet to stay still while the background changes, which can be cool sometimes.

The other approach is if you zoom out the timeline window, way over to the right you will find that each puppet has a finite end. You can grab the end edge and drag back to shorten the length of the puppet. This is what I normally do. No need to do a recording, just drag the right edge back to shorten the length of the background image puppet.

Here is the shortened version afterwards. The puppet will disappear earlier now.