But… there seems to some kind of confusion here. Are you trying to use a hidden / inactive cursor to detect OnBeginCursorOver while not actively using a pointing device to control it?! Because that kind of interaction is done with camera traces + interface. Using cursor for this will be unreliable and inconsistent at best.
You could probably set cursor location to screen centre but… that’s just not the right tool to do it. The traditional method would be close to this:
The above has a redundant extras bit for detecting interactives in proximity. The gist - we trace along a camera vector, send interface messages to the hit components, the components can respond if they so wish.
Here’s another example:
Note this has nothing to do with the mouse cursor.