The Hover Stone plays a major role in Addison's mini-events, where it can be used to support the Hudson Sign Boards at various locations on the map. Normally, you should use nearby materials to support the Sign Boards, but with the Hover Stone, you can support the Signs without using any materials.
How To Use Nearby Materials To Support Hudson Sign Boards
This way of supporting the Hudson Sign Boards is very simple, you can use the nearby materials in any way as long as the signboard stands when Addison lets go of it. There's no need to support it neatly and it's fine to use just one wooden pillar as shown in the video.
You Can Keep Trying Even It Fails
It's not a problem if the Sign Board falls down when Addison lets go of it. Even he says "Whoa! Unforgivable!", you can try to stand the Sign as many times as you want.
You Will Get A Reward If You Succeed In Keeping Addison's Hudson Sign Standing
If you successfully keep the Sign Boards standing, you will receive various items from Addison such as Rupees, Food, or Sleepover Tickets. If you see Addison during your travel, make sure to help him support the Hudson Sign Boards.