The original electromechanical flasher - rectangular metal thing with two terminals - is not smart. Flash rate varies with load current: lamp current heats up a bimetallic contact bar that bends with heat... that openss the contact (turns lamps off) and it cools down, bends back to make contact, repeats. LED lamps with super low current don't flash, just stay on. The expected lamp current gives a normal flash rate. One burned out is slower. Higher wattage lamps heat it faster so it flashes faster.
Two terminal "electronic" flashers will have the fast flash for a burnt out bulb but they "start off" so the first flash is a half second or so after you activate the signal. Three terminal (3rd is ground, the unused green wire hanging near the OEM flasher) are the same but will "start on" and then flash off. I prefer that, I want a signal lit as soon as I slide the switch.
Note there are several three terminal types: some will just blow a fuse instantly when you turn a signal on. These have a second output for a dashlight or second set of signals (trailer?).