You will need to find a copy of the SCSW
On the frame
Front of frame, below barrel, and in front trigger
There is a problem with your question. The Model 36 is a standard weight J frame. The Airweight verison was a Model 37. J frame serial numbers were all numbers until 1969. The serial number you list is for a fixed sight K frame made in the 1961-1962 time frame. That would be a Model 12 Military and Police Airweight.
The serial number on all Savage automatic pistols (model 1907, model 1915, and model 1917, all in .32 and .380) will be found just under the barrel at the front edge of the frame. Early model 1907 pistols will have the s/n on the bottom of the frame, while later model 1907 and all other models will have the s/n on the front of the frame. All .380 Savage pistols will start or end with the letter "B" -- the first few hundred (all are model 1907 pistols) start with "B," while all the rest end with "B." It is not uncommon for the "B" to be misread as an "8." FYI, the "hammerless" model 1915 is the rarest production Savage automatic pistol, and the .380 model 1915 is the rarer of these. About 6500 .32 model 1915 pistols were made in 1915-1916 (approx s/n 130000 - 136500) and about 3900 .380 model 1915 pistols were made in 1915-1917 (approx s/n 10000B - 13900B).
On the frame
The pre 1969 model 60 didn't have serial numbers so if you can't find the numbers it's probably pre 69.
The frame
Frame
Up unitl @ 1957 model numbers were not used. Check inside the frame near the crane, it has a model number, it will be there.
I haven't been able to find one on mine.The Savage model 342 was produced from 1950-1955.During this time frame serial numbers were not required on firearms.The passage of the gun control act of 1968 mandated that all firearms made in the U.S. and abroad have serial numbers,and this was started in the year 1969.I believe that your Savage model 342 were not given serial numbers at the time of production.
On an older revolver, you are not likely to find a model number, since they did not use model numbers. If you remove the grips, you should find the serial number stamped in the frame under the grips.
If the gun never had a serial number, it could be what was known as a "tool box" gun. These guns used a frame which hadn't been stamped with a serial number and was assembled by a worker at the plant which manufactured the gun and smuggled out in his tool box.