My personal theory based on nothing more than the vibe of the thing is that it comes from the Malay/Indonesian word ‘kecap’ (which is pronounced almost identically to “ketchup”), the word for sweet soy sauce. This is soy sauce that is thickened and sweetened with palm sugar, and I could see European cooks attempting to replicate it based on the vague descriptions given by sailors, and ending up with ketchup.