Blank Application pulses in the dock and moves my cursor to the center of the screen

I figure it must be Synergy or BetterTouchTool, possibly? But its really really hard to pin it down. It seems to happen randomly

Do you have enough time to option click (right click or equivalent) the app in order to get the context menu up ? That would let you choose Options>Show in Finder … and hence show you WHAT was causing you grief.

Alternatively I think you can Command-click to do that in one go … but in either case if it bounces once, moves the cursor then this is indeed a PITA to troubleshoot!