When did Smith and Wesson make the 38 short owl head serial number 12747?

No. The Owl's head was the logo of the Iver Johnson company. You MAY see a marking such as .38 S&W CTG- but that marking is the caliber- the revolver shoots a .38 Smith & Wesson cartridge (not a .38 Special). ALL guns that shot THAT cartridge were marked .38 S&W, no matter who made the gun. Smith & Wesson owned the name of the cartridge- they invented it.