All my German
dictionary of surnames has is STECK.
a) Cognomen for a stiff or crude person (from German
"Stecken" = "stick")
b) Someone who lives by a pasture marked out with sticks
Now the CH-version is related as "stecken" (to stick) is to "stechen" (to sting).
About the GH-version I don't know, it could mean something like "one who lives near a footbridge (Steg)", but would then etymologically not be related to "Stecken".
Sorry, this is all I can find. Try behindthesurname.com or ask Menke; he usually finds out a lot.Andy