AlpineRAM

Forget the OD switch wire for the moment- if that was the problem you would see OD off illuminated on the dash.

Pin21 (brown wire) is grounded by the PCM.
You did measure resistance, this checks out that there is a connection and also there is the coil of a solenoid.

Now route a wire connected to Pin21 into the cab, to a switch, connect other end of switch to ground.
Install jumper wire pin 3 to 5 instead of the trans relay.
Test drive, at sufficient speed actuate the switch. Does the trans shift into overdrive? Simple Yes or No question!
The other suggested test od driving with OD off and watch for TC lockup - done yet ? Simple Yes or No question!
If OD off test already done - Does the TC lock up? Simple Yes or No question!

The same grounding test can be done on Pin11 , this controls the TC lockup solenoid.

Yes, the OD housing can be removed from the transmission, but it is better to do the tests I described first.
Then maybe a pressure test (depending on the results of the electrical test stuff).
Only if those results show that you have a mechanical malfunction remove either OD or transmission.

Cpower24v

AlpineRAM

No, I mean that you should pull the trans relay and install a wire between where pin3 and pin5 of the relay go.

The switch is a simple on/off switch. Tee a wire into the brown wire going to pin21 , route that into the cab, attach on/off switch (in the off position), connect other end of switch to a good ground.
Drive up to a speed where you want OD, flip switch to on, and see if it goes to OD or not.

Cpower24v

AlpineRAM

Yes, if it does go into OD you know that the PCM does not command OD- then it's to find out why. Either some sensor input prohibiting it, or a failure in the PCM.
If it does not shift into OD you know that you have to fix that first.
Proper diagnosis on vehicles works like that- you try to isolate different possible sources of the problem (not going into OD) and determine what can influence it.
So, since OD is controlled by electronics- if we override the electronic part with some wire and a switch we know if the mechanical part works or not. So we have already saved about 50% of the cash compared to the parts scattergun approach (throw parts and labor at it until it's fixed while throwing away usable parts)

Cpower24v

AlpineRAM

OK, pin21 is the OD solenoid, we now know that this works fine. You still have no lockup, but you can install a second switch and wire it like the first but to pin 11 on the pcm.
This is the manual lockup switch. Then you will know if your lockup works hydraulic/mechanically.

It seems like your PCM does not command OD and lockup at this moment.

Maybe you can try to read out the values for vehicle speed and throttle position while driving. This could tell you if for example the TPS has fluctuations big enough to not let you get OD and lockup.

Cpower24v

AlpineRAM

I do not know if the Edge gets the RPM from the PCM or the ECM. We are interested in the PCM side here.

You can use the same ground, all grounds are the same, as long as the wire is thick enough. (And I assume you did not use telephone wire)

Basically- if those ground switches both work, no need to pull the tranny or OD unit. Works as designed, gets wrong commands.
You could get a cheap OBD2 bluetooth reader and use an app like torque to monitor the values we're interested in. If the PCM thinks that you move the go pedal a lot it will not lock up. So it is helpful to read out what the PCM sees.

Cpower24v

AlpineRAM

You will need a separate wire and a separate switch, but can use a common ground for both switches.

Or you can swap the pin21 wire to pin 11, and see if you have lockup in 3rd. (You can't test for full functionality of the hydromechanic part with just one switch because you need to command 2 solenoids. )

If I read you correctly you had a gearchange when grounding 21 (applying the switch) but no lockup.
So if you swap the wire to 11 you will achieve lockup (if the hydromechanic part works) but not OD since you do not apply both solenoids.

You must not connect pin 11 to pin 21! So either 2 wires and switches or move the wire from 21 to 11.

Cpower24v

AlpineRAM

Pin 21 is overdrive, and you do not want to shift from drive to OD with the converter locked. So either keep it out to OD with the OD off button and activate pin11, or get up to 40+mph on level ground, activate Pin21 (od without lockup) then accelerate to 50+ mph and activate pin11 to achieve lockup.
There is no need to deactivate 21 before activating 11, it would actually be a bad idea if done at too high speeds- it would downshift from OD to D and then lock up the converter- good engine braking at high revs!

Cpower24v

AlpineRAM

Now we know some more things:
A - the transmission itself works as designed.
B - You mistake converter lock for OD, a lot of people do that.

C- we need to find out why the PCM does not activate the OD and the lockup.