I have opened a few Playstation 2 consoles to fix or clean them so far and I have never seen this weird little board before. It is connected to where the ribbon cable for the front panel (power/reset and eject buttons) usually goes and to a 2-pin connector that is usually for a cable that comes from the optical drive. Now those two cables are instead connected to that board.
It really looks like a hardware patch to fix some sort of problem of this particular motherboard revision. There is also a slight possibility that this is homemade, who knows.
The PS2 that this comes from is a PAL SCPH-30003 with motherboard revision GH-012, sub-revision 1-682-236-11.
Motherboard:
Weird little board connected to the motherboard:
Zoom on the little board (front):
Zoom on the little board (back):






