I had this problem a week back. What I found on my 83 300TDt was the check valve was under the passenger side rear cladding that fits over the tire well and rear seat belt attachement point. Had to remove that panel to get access.

Boiled and flushed the check valve which was clogged shut by washer fluid crystals.

Clue is when you hit the rear windsheild button you should get spray right away, if not and it takes 10 seconds the check valve is open, if nothing, then the check valve is stuck shut.