It is the climate control switch connector, it locate inside dashboard.
When you set the temperate above "COLD", the heater will start. It will mix
with the cold air depends on what temperature you set (lower temperature
less hot air mix with more cold air). If you set it to "COLD" , heater will
turn off and will be 100% cold air.
Recently did you adjust anything or install anything that require to remove
dashboard? You mentioned when you turn to max cold you feel still not as
cold as passenger side but is it colder than before? Do you leave the
engine run long enough to see the difference? How about the air-con vent
adjustment? Open to max?