I am afraid that no one can give anything more solid than an opinion since etymology is a slippery fish where few clues are provided for comparison.What's your opinion?
Komban wa, Flaminius San to Shiremono San.I looked it up in some ordinary Japanese dictionaries. They simply introduce two opinions about the derivation; [目門 ma(eye)+to(door/gateway)], [間戸 ma(space)+to(door/gateway)].
Edward S. MORSE (1886)You should ask yourself: what is or what was "mado" at the time when this word has been introduced? Do you think traditional Japanese houses had "windows" as they are intended nowadays?