Flashers 67 barracuda

The simple answer is, "there is no relay." Not as such.

"Basic" that is original flashers (and also the voltage 'regulator' / limiter for your gauges) work on a little heater element, wrapped around a bi--metal strip. You turn on the turn signal, current goes through the flasher and bulbs

The heater element heats, the bimetal warps, and breaks the electrical contacts. This disconnects all current including the heater, shutting off the bulbs.

The bimetal strip cools, warps back and makes contact, and "we" start all over as the bulbs light up once again.

There ARE heavy duty "truck" flashers, that contain a relay. And some vehicles (Old Ford Couriers) used relays in the signal system

This one, with the cover removed, is one. Nothing like this ever came in these cars