I am thinking, 1970's, probably a house brand saw, from JC Penney, Monkey Ward's or something similar. Just by the style of it. Imported is almost certain. Japan maybe.
They all use a piston or at least a crank and sliding block, to drive the blade.
No belt means direct drive, one speed. Probably too fast.
Or rather a speed only suitable for very thin, very light stock.
Many saws were made this way since the invention of the electric jigsaw. Puzzles, toys or trim from 1/4" stock and thinner, the only real use.
The blade is likely a normal 6" coping saw blade with pin ends, unless there is another blade clamping scheme I can't see from here? Thousands of jigsaws use 5" pin end blades.
I can't believe you went to a warehouse store and asked questions about a jigsaw?? heeheh
Asking any employee a serious question in one of those places is tantamount to child abuse, you know.
They hire them off the street for minimum wage and none of them works there long enough to learn much. Where is the bathroom or the front door? Is about the extent of knowledge you can expect in a warehouse. Asking them questions just irritates them, and wastes your own time.
There are ac drivers now that can control the speed of the motor.
Until fairly recently ac drives were so expensive only industry could have them. But lately the price has finally come down for fractional horsepower motors.
With a slower speed you can cut thicker stock and the blade won't overheat and lose its temper, go dull in a heartbeat and/or break, near so often.
yours Scott