most sears allstate motorcycles were built by bridgstone motorcycle. they also built bikes for wards and firstone. most wrer two stroke engined small bikes in the 125 and 175 c.c. class. sears also sold an allstate car, which was a rebadged henry-j.
Sears sold a lot of small motorbikes between the 30s and the 60s. They came from Bridgestone, but also Puch, and some other small manufacturers who were not otherwise available in the US. They were mostly rebadged with the Allstate brand.
I saw a catalog from the 30s that showed the ‘Whizzer’, which was basically a big bicycle with a little motor mounted in the frame. (Google ‘Whizzer’ and you’ll see them–they are being made again today!) So the bike they sold in 1964 was not their -first- motorcycle. But 1964 was the time of the ‘Honda revolution’, when small Japanese motorbikes were suddenly becoming popular in the US. These came first from Honda, and then from Suzuki and Yamaha, and then from Europe.
They did sell Allstate and if I remember rightly they might have sold Cushman also.
Around 64 or 65 was the first Allstates made by Gillera, before that they were made by Puch