Look under the Mouse, there should be a Bluetooth pairing button...
typically you hold it in for a few seconds, so the mouse knows to be in pairing mode, then initiate the search as you did before.
If the mouse is already listed under paired devices, you may need to delete it before doing the above, but I would just try the above first.
If it asks for a password, it is typically "0000" (4) or "00000" (5) or "1234" unless your manual says differently.