I have several motorcycle projects going on right now and I put the simplex toward the back of the shop, will have to drag it out again on Monday to take more pics, but I think the transmission is not the correct trans, you are correct there is no clutch pedal but the trans is a clutch setup, not automatic....I got a feeling I bought a hodge podge mix of parts, one fender is painted , the other is chrome..I have a feeling the frame is a 52-53 and the engine is a 48 and not so sure what the transmission is ....
For my purposes it is not important as I am going to build it into a military bike, possibly with a side car however I am going to do it without molesting the frame at all. I hope to have the shop cleared out next week and start blasting the paint and rust off of everything....