Ok, there are not separate mode doors or actuators for the left side dash vent, only one mode door for all the dash vents, so it will not be a door or door actuator.
While possible it is a clog, if this was not an issue before replacing the heater core, it is not likely to be the issue.
The most likely issue is the air duct going to the left side dash vent is disconnected, either at the vent or further back where it come off the hvac housing. You can pull the vent to feel thru there to see it the duct is connected and if it isnt, you may be able to reach up thru the bottom of the dash to reach it and connect it.
If it is connected then you will likely have to pull some of the dash to get to the ductwork to locate the disconnection and the reconnect it.
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