Is a milliner more likely to be a woman? In the millinery section of trade directories, quite a few are.
Looking for any Connor:
South Bend and Mishawaka directories in the Millinery section and alphabetical names:
1903 nothing under Mishawaka, but South Bend city directory has Conner, Nathan (Eva) wks S W Woollen Co, res 435 N Lafayette
1905 has Conner, Eva wid (Nathan)
1903 has Connor, George G (Delia M) draying, res 508 E La Salle Ave
would expect a milliner to be female but she's not listed in the milliners section
1901 no Connor or Conner. No Connor or Caldwell or Brown listed under Milliners.
Hmm, was Connor an invention too?
Sandra have you come across any newspaper entries for Brown & Connor, or Caldwell & Anderson at all?