First thing I "think" I see is an aftermarket replacement water valve, unlike what's on our '72 Newport. On an OEM-style valve, the cable goes into one of the clips in #9 above. The clip goes onto the "spindle" of the valve, and can be moved in the clip, which is where the "self-adjusting" part comes in. It's not a firm attachment, but one that can move as needed.
IF your car is like our '72 Newport, it has a two-piece cable, with an a/c compressor switch in the mix, too. The a/c compressor runs ALL THE TIME, but if you move the temp lever slowly, about 1/2 way through its travel, you'll heave/feel a slight "xlick", which is the compressor switch turning off. This switch is apart and separate from the dash-mounted a/c switch.
Which is another reason the engines in these cars can feel a bit "doggy", with the a/c running all of the time, normally, even if the dash switch is "OFF".
Once you get the correct clip, open the valve manually and then move the heat lever to MAX. Let that be the total travel of things, so that's where you put the eable end into the slit in the new clip.
What I did on our '72 Newport was to move the heat lever to the right, just past the "click", then take that as "OFF" for the heat lever. Still enough water flow for good heat, at least in our DFW climate, in the winter. But all it would take to undo what I did was to move the heat lever back to "OFF", which put things back "as designed".
On these cars, when the a/c controls are "OFF", the a/c compressor still runs and the fan runs at a very slow speed. Enough to keep some air circulation through the hvac system such that when the "DEF" button is pushed, a quick cloud of moisture does not form on the inside of the windshield, before the heat arrives to evapoprate/elear it off. I guess it works. This is for the factory manual a/c systems. Not sure about the AutoTemp variations or non a/c vehicles.
Just some thoughts,
CBODY67