Drivetrain Overdrive Issue

See if this helps. It's from the service manual.
Transmission Control Switch

The transmission control switch (TCS) is a momentary contact switch located on the floor shift console, next to the gearshift lever (7210). When the switch is pressed, a signal is sent to the powertrain control module (PCM) (12A650) to allow automatic shifts from first through fourth gears or first through third gears only (locking out fourth (O/D) gear). The powertrain control module then energizes the transmission control indicator lamp (TCIL) on the instrument panel to indicate O/D OFF.

On the AODE application, the TCS signal is sent to a transmission control switch module (TCSM). The TCSM sends the signal locking out fourth (O/D) gear to the PCM and turns on the TCIL to indicate O/D OFF.

If the OD light is not illuminating it would appear the ECU isn't sending a signal to the TCMS. Here's the wiring for the OD switch and the TCSM.

http://members.shaw.ca/r-manders/TCSM.bmp

The location of the module is behind RH side of I/P

While testing, did the switch show continuity while depressed (it's just a momentary switch as I recall)?

Does the OD light come on when the button is depressed? If not, check your trans control module. It's behind the glovebox (it's just a little black box a little smaller than a deck of cards). It's what turns off OD (IIRC they didn't have room in the ECU for this so they used a little module to handle it). It should have a label on it with a part number similar to F4ZF-7E453

Good luck.

EDIT: Richard posted while I typed. Great post BTW.