" every so often it will kick into overdrive, with the light on, not down shift to 4th gear, and stay stuck for a while."

Eliot,
You aren't the first to be confused on the AW70 operation. The Arrow Light means that you are NOT in OD, but direct drive 3rd gear. Pushing the shifter button should put the light out (the normal "default" state at start up) to upshift into OD (4th gear).

As Chembrad says, the OD relay is suspect, but here is an outline of the relatively simple OD control circuit, in case you need to dig further:

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 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 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.

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...consider this recent reply to a "check the wiring" suggestion:

"Replaced corroded connector and length of wire with bad insulation. Working perfectly now."

He was having "intermitent" OD failures, was sure it "couldn't be wiring" (that would be "all or nothing"), and was probably on the way to a solid failure.
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Bruce Young
'93 940-NA (current) — 240s (one V8) — 140s — 122s — since '63.