OD operation involves 4 components and the wiring that connects them...

1) Fuse 11 (200) or 12 (700/900) supplies voltage to items #2, #3, and #4.

2) The Shifter button/switch turns the OD relay off and on

3) The OD relay controls the Upshift ("OD off") Arrow light and the OD solenoid (separate wires). When the Arrow light is ON, the relay and solenoid are OFF

4) The OD solenoid allows OD engagement when ON, (this is the "default" OD relay/solenoid state at Key On)

If the Shifter switch turns the Arrow light on and off, then #1, #2, and #3 are OK, and the problem is most likely the undercar wire to the Solenoid (#4) or the wire connector terminal at the solenoid.

Less likely would be be Solenoid itself.
An internal transmission problem is also possible.
--
Bruce Young
'93 940-NA (current), 240s (one V8), 140s, 122s, since '63.