Originally the motor number served as VIN. If the motor is original you can still use the number. If not original you will probably need to ask your taxing authority (Tag).
As stated above the engine number is most often used as a VIN but with that being said when I registered my 32 the DMV in Connecticut(A non ***le state) used the Fisher body number which is on a plate riveted to the firewall. Their rationale was that the engine could be easily changed but the body number was permanently attached. I know of quite a few other cars that are registered with the Fisher body build number. Best bet is to check with your local DMV
My 38's got a VIN tag on the right cowling about waste high. I had another 38 and a 39 with the same thing
My 37 Chevy cars all had 10 digit Vin numbers. The 3 Sedans I have had all started with 12GB and then a series of 6 more numbers. The ID tag is located on right side of the car on the side of the firewall. Not sure what the DMV in Texas requires. In New York one of mine did not have paperwork. They let me do a rubbing of the Vin number and issued a non-transferable registration while they complete their search. After 6 to 8 weeks if that number had not shown being ***igned to another vehicle, they then issued me a transferable registration.
VIN tags used from about 1954 - patent plate, warranty plate, vehicle identification plate, etc were earlier
I believe that there should be two plates riveted to the p***enger side of the cowl. https://www.fillingstation.com/articles/carnumberplates.htm My 37 has the body plate, but not the serial number plate. A 37 cowl I have in storage has what looks like a serial number plate on the p***enger side firewall. I need to look more closely at that in the spring when the snow melts and my shed is easier to get to.
Although mine shows allens, I think they're usually held on by clutch head screws, not rivets (the larger plate that's in the closeup may have been riveted, but not the smaller VIN tag)
Groucho posted the a great pic of the Body tag. When I registered the 37 I told the state trooper inspecting it that the original number was the motor number. Since he was as young as he was this was news to him. I explained how the motor number was not a good idea in the first place since motors got changed and paperwork was never updated. I used the numbers off the tag. Now look at the tag Trim number is repe***ive, so is the Paint and Style. The only good number is the Body No. since it is unique to that body. That number will always stay with the car no matter how many motors you go thru. The trooper then said he would turn in the info since this was the best number to use.