Hi, I just ran a quick experiment and was able to get an Atlas character onto a horse and have the both of them moving, but in an unsatisfying way ! It seems you are correct in your last statement, and even after duplicating the Input Action Asset file from the integration and giving it to Blitz, I was only able to move Atlas and get him onto and off the horse, I couldn't move Blitz at all. I was able to when I activated my XBox controller - the Player Input on Atlas was tied to the keyboard, and the one on Blitz to the controller, as you can see in these 2 pictures :
View attachment 14253
View attachment 14254
One last thought, I had initially tried setting up Blitz myself but ended up just using the demo one, could you try doing the same to see if we get to the same point with that ? I have a feeling something may be missing from your own Blitz.
I know this is not solving the issue, but I hope it can help a little nonetheless ! We're going to need
@Justin 's light on the subject, and maybe an example of this in the Input System integration demo would be helpful.