OK, you guys have convinced me that something is wrong. It is the Ford factory wiring diagram that is wrong. I ran my seat all the way forward and peered underneath. Lo and behold! A 4 pin connector.
I pulled it off and noted the wire colors and sizes, and measured the voltages.
Viewing the seat in an upright position from the rear, the connector has 4 male pins facing you (2 rows of 2), and the plastic housing is wider at the top.
Pin / wire color / function
=========================
Upper left / black / chassis ground.
Upper right / brown-blue / seat buckle switch.
Lower right / green / lumbar power fused 15A.
Lower left / green / seat motors power fused 30A.
========
| G | B |
| + | + |
======
Looking at the pins from the rear of the seat, seat in an upright position:
G = ground, B = seat buckle switch, + = 12V