You have the controls pretty well figured out, but a minor point is the switch. It's not an ON-OFF type, but a momentary contact push-button. Whenever it's pushed, it should "toggle" the relay to it's opposite state.

If you like the switch-controlled downshift, as I do, the control circuit is really pretty simple. It involves 5 components and the wiring that connects them. (Flushing is a good idea too.)

1) Fuse 11 (200) or 12 (700/900) supplies voltage 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 OD are 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 probably 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 less likely) would be the relay controlling the Arrow light (#4) correctly, but failing to activate the Solenoid.
An internal transmission problem is also possible.

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Bruce Young
'93 940-NA (current) — 240s (one V8) — 140s — 122s — since '63.