Refrigerator runs constantly

Refrigerator - Jenn-Air JRS202 Side-by-side (no water)
Problem: The fan never shuts off and eventually, everything on fridge side
freezes.

I have replaced the evaporator fan motor on the freezer side and the
thermostat on the fridge side. It still never shuts off. By turning the
thermostat to its lowest setting, it will shut the fan off, but by turning
it a little, the motor kicks on and then never shuts off. The freezer temp
is controlled by an opening between the freezer and fridge with a flapper
that opens and closes to let more or less cold air from the freezer into the
fridge. When the fridge gets cold enough, the thermostat should shut off
the motor on the freezer side. But it doesn't.
What other part could be at fault? Thank you.

I would think that if you replaced the thermostat (cold control) and this
unit still does this there must be some kind of restriction for air
circulation. Remember it's not just the air damper control (the flapper you
speak of) the air also has to flow through somewhere else.

We've been having problems with some Maytag and Amana side by sides in this
same way, it seems a part of the cowling around the lower orifice comes
apart and restricts the air but I've never seen this happen on a Jenn-air.
There has to be a reason though, you just have to get right in there and
find it.