I think the line from the offending skimmer is blocked. Can you get a snake into it from the pump?
If not, stick a water hose down into the pump basket and then down into the line that goes to the skimmers....push it in as far as you can. Pack wet rags all around the hose where it goes into that pipe, getting the best "seal" that you can and then turn on the water in the hose.
Hopefully that backward flow will dislodge any obstruction.
Since you only have one line going into the pump, where do the two skimmer lines come together? If the blocked skimmer line is furthest from the pump, this likely will not work. What is the psi of the pump in the "filter" position?
If not, stick a water hose down into the pump basket and then down into the line that goes to the skimmers....push it in as far as you can. Pack wet rags all around the hose where it goes into that pipe, getting the best "seal" that you can and then turn on the water in the hose.
Hopefully that backward flow will dislodge any obstruction.
Since you only have one line going into the pump, where do the two skimmer lines come together? If the blocked skimmer line is furthest from the pump, this likely will not work. What is the psi of the pump in the "filter" position?