There is an option in LR publisher to choose a random thumbnail image to show for an album set (not an album), but it does not seem to put any image in there, just leaving it blank. I can choose an image manually, but it is static and additional work. Not sure why the random selection doesn’t work like it does for albums. Any help appreciated!
Random thumbnails are drawn from the album’s (or album set’s) thumbnails/ folder. Since album sets don’t generate images (only albums do), you need to provide them if you want random thumbnails.
Export some representative images at the needed size from Lightroom and then upload them to the thumbnails/ folder of the album set.
Ahh, so that is expected behavior? That is a shame, I thought it was a bug 
It would be so convenient if random images could be pulled from the sub-folders (albums or album sets) and available to be cycled as the thumbnail for an album set, oh well.
How do I request a feature update?
You just did.
I don’t know if it’s possible to do that with Backlight (I imagine it would take a bit of resources to scan all album thumbnails and randomly select for the set’s cover image).
And Lightroom can’t publish images with album sets, only with albums, so the thumbnails folder can’t be populated by Lightroom.
The easiest solution I came up with was to create a Lightroom Export preset. Then select representative images from a set’s albums and export them to a folder for that set. Then just upload them to the corresponding set’s thumbnails/ folder.
Random thumbnails were always a band-aid for being unable to supply thumbnail images to sets. The technique for assigning thumbnails, shown in this video, is not our preferred/recommended method of thumbnailing sets.
https://blog.theturninggate.net/2021/01/24/upload-custom-images-in-backlight-3-2/
So this video applies to albums, but not sets. Does the same technique work for custom thumbnails for album sets?
Also, if this is not your preferred/recommended method, what would you recommend?
If you’re in an album, and access the same side panel in the large-image view, you will have an option to assign the image as thumbnail to parent sets, as well as to that album.