The complete Oxford English Dictionary traces the word jaywalker back to 1917 and labels it originally US. There is a cross-reference to the word jay which has a number of slang senses. The relevant one is a stupid or dull person or a simpleton. Also (as adjective) dull, unsophisticated, inferior, poor. This is labelled US colloquial and there is evidence of use from 1900. So persons who stupidly ignored traffic regulations were given (in Boston, it seems) this compact name.
