When it is quiet in your neighborhood, give this a try.

Remove the glovebox to get at the relay. Remove the cover from the relay. Turn on the ignition and close the doors so you don't listen to the dinger.

Test the button alternately operates the relay and douses the OD-OFF light. Leave it in the position, with the dash light on. Using an ice cream stick or other insulated tool, close the clapper on the relay manually. Listen closely for the clacking sound BELOW the floor, under the shifter.

If the sound is there, the solenoid valve could be operating electrically but hydraulically clogged. Solenoid will need to come off.

If no sound, then the most common trouble is the white wire under the transmission tunnel has corroded in two at or near a bullet connector where the solenoid plugs in.

But, it could also still be the relay, so verify operating the relay puts 12V to the white wire that attaches at terminal 87, before crawling under your car.
--
-K (hope springs eternal)