The OD operation involves 5 components and the wiring that connects them—

1) Fuse 11 (fused voltage supplied to items #2, #3, #4, and #5)

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

3) The OD relay (controls Upshift Arrow light and Solenoid) (separate wires)

4) The Upshift Arrow light (ON means relay and solenoid OFF)

5) The OD solenoid (Allows OD engagement when ON, the "default" Relay state at Key On)

If the Shifter switch makes the Arrow light (#4) go on and off, then items 1, 2, and 3 are OK, and the problem is most likely the undercar wire to the Solenoid (#5) or the wire connector terminal.

Less likely would be be Solenoid itself.
Also possible (but very unlikely) would be the relay controlling the Arrow light (#4) correctly, but failing to activate the Solenoid.
An internal transmission problem is also possible.

And as the V70 dude says, get a Bentley manual.
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Bruce Young
'93 940-NA (current) — 240s (one V8) — 140s — 122s — since '63.