Ghast Lead Mechanics

The "Happy Ghast" is awesome and I love it. Although, there is an improvement that would make it fantastic. I was building a vertical chamber for the Happy Ghast because I thought of the idea of a smooth elevator. To achieve this, I would make the Happy Ghast chamber, or the Elevator shaft, and have a water elevator right next to it with a mob that can be leashed. This way, this Happy Ghast platform the player can stand on could be dragged by the mob in the water elevator to go up and down. However, once the player stands on the Happy Ghast, the Happy Ghast will not move, even with a lead pulling it. The lead will just break.

I would love it if the Happy Ghast can be influenced by leaded mobs while the player is on the top of it so things like this could be made.