WW2 Phone WE653AX

[TelePlay]

The back board may have been needed due to the way the wall was constructed where it was to be mounted. A larger back board spreads out the gravitational forces and can span more supporting cross members in the wall. I would assume these are quite heavy compared to the 354 and newer wall phones.

As for the circuitry, wouldn't this be similar to a 302 circuit but with the addition of leaves connecting the front housing to the back circuity?

Are the leaf/contact switches clean so the dial and transmitter is in the circuit? Others can help you trace the circuit to make sure the dial along with the coil, ringer and capacitors are wired correctly and working. Being a gutted pay phone, this can't be much more than a 302 circuit given the 101A and B1A ringer.

I could not find a wiring diagram but that does not mean one does not exist in some BSP.

Where did you hook up the line cord, L1 and L2 on the coil or somewhere else?

[Ron6519]

There were wires going out of the phones back.  Two were connected to terminals(the third one was twisted around the other two and never made it back into the phone.).  I just tried putting the green and red energized wires to those terminals.  When the first combination didn't work, I reversed them.
I don't know if that third wire was actually connected at some point.  I'll check the wiring diagram on the inside of the phone for any hints. My wiring diagram reading skills are, rudimentary.

Got it working.  Dials out and receives calls.  Just need to get it to ring.  If it's the same as the 500 series, we should be good.

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[TelePlay]

There were wires going out of the phones back.  Two were connected to terminals(the third one was twisted around the other two and never made it back into the phone.).  I just tried putting the green and red energized wires to those terminals.  When the first combination didn't work, I reversed them.
I don't know if that third wire was actually connected at some point.  I'll check the wiring diagram on the inside of the phone for any hints. My wiring diagram reading skills are, rudimentary.

Trace those wires back into the phone. One (colors don't matter) should go to L1 or L2 on the coil and the other should go to the other terminal (L2 or L1) on the coil. If you can't trace them, trying attaching the line cord (red and green) to L1 and L1 and with the front housing on (so the dial and transmitter circuit is in place) then try it.

The 3rd wire may have to be shorted to either the red or green terminals.

If you try using the phone without the front cover on, it won't work.

Post larger sized photos of the wiring so they can be enlarged for examination/tracing, use 2500 by 2000 pixels.

Also, there are members who know this stuff a lot better than I do so I hope they read all this and start to help you out. This is a unique phone and may need help from those who know both pay phones and desk sets (it's a combination of both, sort of).

[Ron6519]

And now it rings.  Issue was a spring was pushed against one side of the coil and the bells needed to be adjusted so the striker could reach them.
Cosmetics are next:
- A good cleaning
-super glue a crack on the receiver
- get the missing phone number holding item in the middle of the dial
-remove the rust from the coin slot blank
-Maybe paint the whole cover unless I can match the paint on the blank after it's de-rusted and painted.

The paint looks to be a satin finish.  Trial and error on the blank should be relatively easy.
Again, thanks so much for the input and feedback.  Without it, the phone would have probably set on a shelf after I futzed with it for a time..  Finished, it will be mounted in the kitchen as the secondary phone.  In time for Thanksgiving where the kids last, year played with the 500 desktop phone all night. 
This will blow them away