Same as BF1942, BFV uses "background.bik" for the background video played in the background. Some mods don't use a video and use a background.tga file instead. If it's a texture BFV recognizes, it will be loaded if it's got the correct name.
That's how the vanilla BFV mod folder is set up, so it's safe to assume mods would use a file like this too.
However if for some reason still doesn't work (background.bik goes in the Movies folder of your mod), then the maker of the mod might have altered the path for the video in the menu's meme files. Which will not be as simple to fix unfortunately.
But you mentioned that you are the maker of the mods that have this issue, so meme file changes seem unlikely at this point. So most likely just missing the background.bik file.
I have cameras in your head!