There is no "OD housing" on the tranny. The OD is all internal, except for the solenoid that controls it, which is on the left side, just above the pan joint.

You hear the relay click -- how about the solenoid? You should be able to hear it by leaning out the door, or have someone work the switch while you kneel doen on the driver's side.

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.

BTW, in case you are tempted to drop the pan for a filter change, my advice is, "don't do it". I always used to drop the pan to replace the filter screen. But I never - NEVER - found a dirty one, so I stopped looking.

Then I learned that Volvo doesn't think it's worth the effort either, per this Technical Service Bulletin posted by Gregg Shadduck on Feb. 10, 2005...
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TSB 17106
Dec 1990

"ATF filter cleaning deleted"

for 200/700/900


for all those AW 70/70l/71/72L transmissions
and for ZFHP22
(Does NOT apply to BW*)

"It is NO LONGER REQUIRED [capitalized in original] to clean and inspect the Automatic Transmission Filter..."
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Bruce Young
'93 940-NA (current) — 240s (one V8) — 140s — 122s — since '63.