In a "normal" world, you should not need to worry about wiring and cables- they should just work. I thus think the problem is with your switch box- what is it please? Model, type of switch (manual/auto)?

My thinking is that the switch box is using two different cabling methods as UTP cable only uses 4 cores and, as we used to do in the long past, we used to wire 4x cores for one connection and the other 4x cores for another connection thus using one cable to connect two devices and at each end we had a special device which would split the cores back into two separate connectors. Try the different cable combinations on each of the two connectors of the switch box and I recon one cable connection will work with one of the ports and the other cable connection will work on the other port. But without knowing what the "switch" device really is only allows me to guess on your behalf.