Hi BT
The serial number on these machines is stamped into the comb, either centered or to the right. Lift the front edge of the machine up so you are viewing the keys edge-on and the serial number should be visible between the top two rows of keys

Hope this helps
Sky
We humans go through many computers in our lives, but in their lives, typewriters go through many of us.
In that way, they’re like violins, like ancestral swords. So I use mine with honor and treat them with respect.
I try to leave them in better condition than I met them. I am not their first user, nor will I be their last.
Frederic S. Durbin. (Typewriter mania and the modern writer)