Thanks for the ideas.
The actualy connector has room for 16 pins, but one is solid, so only 15 pins on the motherboard and 15 openings in the "molex-like" connector. It uses a ribbon cable in-between the connector and the circuit board that has the momentary on/off buttons.
By looking at the back of the circuit board, each button has four (4) traces that lead to the wires.
Am I better off finding a "spare plug thingy", splicing into the ribbon cable, cramming some wires into the existing 15-pin connector on the motherboard, etc.?