Ok so, it works partially. The autonomous movement pauses well if you place a draggable event on a tile in which there isn't any other event, but if you place a draggable event over another event, the draggable event goes back to its position and the autonomous movement doesn't resume and it remains paused. I noticed that this issue doesn't appear if you set Stackable Object to "true" in the plugin parameters.
I'm sorry if I'm bothering you, but maybe I found another little issue. So, when I drag a draggable event over an impassable tileset (not event), the draggable event doesn't snap back to its position and it remains blocked over the impassable tileset without moving at all. You can encounter this issue if Stackable Objects is set either to true or false.
Re-uploaded the latest versions again. I added a new feature to both that blocks objects from being dropped on impassable tiles now. I fixed a typo I made in the last update & I'm hoping that fixed the autonomous movement issue on your end. Even with the typo it already works right on my end for whatever reason. As soon as an even snaps back it starts moving again. It also works with stackable switched on for me. The events start moving after the drop. Not sure why its not working for you unless maybe I uploaded the wrong file before. Try it again.
I re-downloaded the file. Now the draggable event snaps back to its position if it is placed over an impassable tileset, but the autonomous movement remains paused. I don't know why it is not working for me, but it is working for you. I recorded a little gif to show the issue: https://imgur.com/tVMfFd9
Ok, so after updating my test project files to 1.6.2 I was able to reproduce the issue. Seems to have been cause by a typo. A missed capital letter in a variable name to be exact, but fixing that seems to have once again fixed the issue on my end. Try re-downloading the file again & let me know if it doesn't work.