Air or heat will not switch from lower to upper dash vents

Question edited for clarity and toss in some upper CASE letters.

There are all in one place under the centre of the dash.

https://www.google.com/search?q=2013+Lincoln+MKS.+Mode+control+actuator+location

I believe you mean "BI-LEVEL" mode, which means it should blow air simultaneously out of the dashboard registers and the lower register. The Temperature of the air blowing out of both of them is regulated by the temperature preset.
Does the fan still blow when you move the switch to BI-LEVEL? If it does but the air comes out of the DEFROST registers, that means your diverter is not functioning correctly, most likely due to a vacuum leak under the dash. If the fan shuts off in BI-LEVEL mode but still operates in HEAT mode, your selector module is bad. If the fan shuts off in BI-LEVEL mode and in HEAT mode, either your engine coolant is not hot enough to provide heat (automatic function), or the temperature sensor for your climate control system has failed.

This sounds a lot like a door actuator it is locate behind the radio part od the dash when you switch the vents like to the floor upper dash do you hear a clicking sound? put your ear to the middle of the dash where the switch to the heat / cool is and listen for the clicking sound when you change the vents direction. If you do it's the vent actuator you will have to remove the face part of the vent and it's in behind that it is usually a white plastic box it may be black but most are white. The cost is about 90 to 120 Canadian dollars.
Hope this helps good luck.

MODE DOOR NOT SWITCHING FROM AIR TO HEAT IT'S UNDER THE DASH THERE ARE TWO 1 THAT WORKS THE VENTS ONE THAT WORKS THE DOOR FOR THE HEAT AN AIR IF VENTS CHANGE FROM DEFROST TO DASH AN TO FLOOR IT IS THE MODE DOOR actuator

Is the coolant level full? What does the temp gauge read on the dash? Can you hear a difference in air flow out the vents if you switch from full hot to full cold?

I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_d728a59f986299fa

There is a blend door acuator which moves when u change your settings. Its a electric motor. Down under dash, Will need a mech and a heating and cooling diagram to find where the motor is,

The switch that controls the defrost, heater and vent settings have gone bad and needs to be replaced. Auto Zone should have that part or you can do the Salvage Yard for around $10.00. The switch that controls the setting has a diaphragm and when it fails, the vacuum from the air lines starts to make the sound you hear and there is not enough pressure to engage vent doors. It take about 20 min to replace from start to finish and your only going to remove two screws from the dash over the instrument panel, the trim panel around the stereo and climate control just clips in place. You don't have to remove the trim panel, it's to much of a pain. the climate control is held on by 4 bolts and the vent setting is held on by one bolt. Once you have the climate control panel unbolted from the dash, disconnect the vent control vacuum lines and then replace the vent control switch. Once replaced, put everything back together in reverse the way you took it apart. Good luck and check that the new vent control works before you put everything back together, just be take caution when you have the engine running to check.

try to check if the vanes works well also try to check the A/C filter

Can you hear anything moving in heater when you move the switch to other settings? If not then the blend door is not moving to redirect air flow. There is three things that could cause this, 1 the control switch is bad or 2 the blend door acturator is bad, and 3 linkage for the door has come unhooked or broke, most likely its #1 or #2. First you need to find the blend door acturator and test light the wires to it, there should be 3, 1 hot with key on 2 only hot with switch moved, and 3 ground. If you got power from wires than the acturator motor is bad, if no power switch is bad.

Had the same problem. believe it or not i changed the gas cap and got heat all around. something about pressure.