That one is the unique-to-Australia version, which like the North American luggage rack cannot be used with a rear-mounted spare tire. Only the unique-to-Europe rack could be used with a rear-mounted spare tire. All three racks are shown in Chapter 19 of the 1932 Ford book. Attached is a photo of a European rack attached to the back of another surviving Danish Briggs-bodied Tudor saloon like yours.
I saw an Australian phaeton body the other day and was reminded of some photos that I had buried away from when I first started to look for a '32 phaeton back in the late 1960s. They're shown below. The photo with two '32s, a '33, and a Model A and the photo with the phaeton with the unusual top arrangement and arrows painted on the side are of cars then in Australia. The other photos (those of a basket case body and the color photo of a complete car) are of two that were owned by a fellow in New England and for sale at the time.
I did not buy any of them as I waited to find one of North American origin for sale and have no idea where these Aussie versions ended up.