Since you can isolate each suction line, I would shut off the bottom drain and the working skimmer so that you only have flow from the problem skimmer. Remove the basket and start feeding "quality" masonry line down said skimmer until said line shows at the pump strainer. A helper is needed just in case the end deciders to enter a hole in the strainer and mess up the impeller.
If that is successful, turn off the pump, and tie on a quality piece of heavier line, at the pump strainer which is now removed and slowly pull that back out from the skimmer.
Again from the pump, attach a 3/8 inch washer onto the heavier cord but do so with a knot in the middle of the line.
In short do not cut the line, Slowly pull heavier twine and washer from the pump to the skimmer; if you get any resistance then you and your helper will need to do a pull/pull, skimmer to pump in order to dislodge the obstruction.
Hopefully the washer will grab what ever it is and let you pull it out from the skimmer.
Washer passes through with no resistance? Use a half inch washer next, then a fender washer but nothing with a diameter of more that 1 1/4 inches assuming that you are dealing with a 1 1/2 inch pipe.
Do NOT skimp and try this by just pulling from the pump to the skimmer or visa versa; you MUST have a way to pull from either end or you could have a real blockage on your hands.
Once she is clear, invest in two 1 1/2" pvc plugs.
You might try the shop vac to suck that first masonry line from the pump to the skimmer if you have no helper.
GL, and keep us informed please.
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