If your piece was made in the 1920s - the serial number would be stamped into the butt strap. However - it will always be found under the top strap - remove cylinder to see this "primary" s/n location - and most times under the left grip panel on the bottom strut of the grip frame.
The ENTIRE run of "Auto Ejecting/Automatic" H&R revolvers have "free wheeling" cylinders. As you posted, H&R advised that the firing pin be nestled between cartridge rims on on a fired primer when carried.
Check out this "instruction manual" found inside a box from the 1880's: