This is a portion of my dock on OS X. (You’ll have to click it, since the important part is truncated by this forum).
The SketchUp icon on top was dragged into place from the Application file as a quick-launcher, just like every other icon on the dock.
However, when I click on it, it doesn’t launch itself, it opens a new instance of SketchUp on the dock, the one you see below with the dot indicator on the left. When I quit SketchUp, the bottom one disappears and the top one remains.
Obviously all the other apps on my dock behave normally, launching in place with a dot to the left to show they are running.
Really just a persistent annoyance… since I use the dock for quick app switching and their location is muscle memory for me. The SketchUp icon gets clicked a lot and nothing happens until I realize (again) that it’s somewhere on the bottom with other incidentally running apps.
I wasn’t aware of the 3rd way to dock an app that you just described.
For whatever reason, that worked!
So I had to run SketchUp.app, which creates two dock icons. If I right click / “keep in dock” on the second one, I can manually remove the first, then launch and task-switch from the second from then on without any duplication.