Question I'm wondering why this fbx's clothes are not part of the animation

I ripped some fbx's from a game called Gloomhaven Digital, to add those assets to another game called Tabletop Simulator, some of their assets have secondary objects other than the main mesh, for pieces of cloth and the like, in some of them they are following the animations properly, in some of them they are just floating there, I am new to all of this, and I cant detect what the difference in both kind of models is, they seem to be all fully rigged and properly parented in my inexperienced eyes (and they are both fully animated in the original game), can someone take a look at it and maybe point me in the right direction on how to fix this?
(example of piece of cloth following animations vs not following, in 2 skeleton models from the same game

)
I'm dropping both skeletons fbx here just in case someone wanna take a peek at them and help me figure out why one is following and why the other isnt.

If its just a case of the cloth not being animated, then I would appreciate a quick tip on how to do it myself, I tried following a tutorial but they all want me to move on the timeline and move the piece of cloth around, so it transitions, however for whatever reason, trying to move the cloth around wont work, it seems to be fixated in place on the skeleton.