MadMan -
Welcome to Vacuumland.
I started researching Cadillac about 10 years ago, and I have a list of some of their models (based on years of advertisements placed). The 12x models tended to be the 2nd tier of cleaners, that is, the "B" line - loss leaders behind the top of the line.
Cadillac heavily advertised in the back pages of women's magazines and housekeeping/decorating magazines. You would write away to an address, and a salesman would follow up with a visit to you. Cadillacs tended to be in the low- to mid-price range of vacuums. Rarely did they reach the price of Hoovers, Electroluxes, Kirbys, etc.
My incomplete list turned up a model 124, a one-speed model with a headlight and turn-knob height adjustment; this was from a marketing brochure from a company called Marshall-Wells, dated 1939. So, possibly, your model is from earlier than the late 30's. Is yours a one-speed? Is there a switch to turn the headlight on and off? Those switched headlight models (and another switch for 2nd speed) tended to be on the "A" line models.
