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There were two types of Stockinger, (1) hand and (2) machine.
(1) Stockinger was a name for a hand frame work knitter, hand frame worker, hand knitting machine worker, who set up the yarn in a hand frame by inserting bobbins and threading thread through guide, and operated it by turning a handle or with treadles.
(2) Stockinger or Sox Hand, was a general term for workers who were engaged on sock knitting frames, e.g. Cotton's patent frame hand, automatic seamless machine hand, XL hand.
"A Dictionary of Occupational Terms"
Stan