See 3452.1-02 in the ETM for the DSC button info.
To connect to the DSC button, we use another stock connector. These are part #61-13-8-380-696. They come empty; you need 4 pins for each, part #61-13-0-005-197. These are the same pins used in the DME connector and the instrument cluster connector, hence the total of 10 in my parts list: 4 for the harness adapter, 4 for the new plug for the DSC button, one for the DME connector and one for the instrument cluster connector.
Note the orientation of the connectors. Both have the smooth side facing us; on the opposite side, both have the rectangular cutouts for the pin sleeve latch prongs and the overall hinge latch for the connector. The harness MUST be connected in this manner. This inverts the pin numbering; pins 1 and 4 are swapped, and pins 2 and 3 are swapped. Don't get confused by the numbering; just use the picture above.
You should also wrap a piece of electrical tape around this connection to supprt it. It won't just fall apart, but it's also not latched; the only thing holding it is contact friction.