App Stellarium and hourly wobbling motion of Neptune
This appears to me as just the consequence of having an altazimuthally mounted “camera” (the simulation). Objects are tilted towards the left when they rise, towards the right when they. set. You can verify that easily by looking at the Moon when it rises and sets from your own place. This is due to the horizon being “tilted” with respect to the Earth’s plane of rotation (unless you are exactly at the pole).
I’m not super familiar with Stellarium, but as far as I know, there’s a way for the observer to not be located on the Earth, or at least, you can change the latitude of the simulation. Try that, and if you set yourself as being at the Earth’s (north or south) pole, you shouldn’t see that anymore.