The safety, if it is unmodified, is forward to Safe, rear to fire. It does not auto return to safe when the action is opened. That behavior seems more like the common errors of reassembly of a 3 position safety.
I have also heard it said (outside this group) that LC's did not put the 3 position safety on Fw guns. Am I incorrect thinking that the Fw prefix on the serial is indicating Featherweight?
12 ga, Hunter Arms, Fw 36640, hammerless, extractor 1921 per Look up.
For comparison, I have-
16 ga, 206162 hammerless extractor (not in table)
20 ga, FwS9478 hammerless extractor (1919?)
Neither of the latter two are marked with mfg on the barrels.