The horn is actuated when the horn button (or something else) provides a ground to complete the circuit so only one wire is required. If cutting the wire leading into the column stopped the horn the wire between the cut and the steering wheel is grounding to something (probably inside the column. You will need to replace the wire inside the column (not as hard as it sounds) or add a horn button as you mentioned. The horn button basically has two wires, one from the horn relay that originally went into the column and a second from the button to ground.

1949/50 3600 Project
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