I assume that what you refer to as side flashers are merely the front side marker lights. They do not work as turn signals. They light up whenever the parking lights or headlights are turned on, together also with the red rear side marker lights (which might have been disconnected in a European car at some time, depending on the local legal standards).
These side-facing devices make the vehicle's presence, position and direction of travel clearly visible from oblique angles.
The law in the U.S. initially required lights or retroreflectors on vehicles made after 1 January 1968. This was amended to require lights and retroreflectors on vehicles made after 1 January 1970.
Front amber side markers in the United States may be wired so as to flash in synchronous phase or opposite-phase with the turn signals, but they are not required to flash at all, and they actually do not flash on old Mopars.