If you have LED lighting in the actual turn and tail lights, they may not create enough heat to activate the flashers (I have some concerns about the LED flashers as well, nothing is as good as it was 3 years ago). There are resisters you can add to the LED turn and tail light wiring to assist the LEDs with the flasher applications. Should show up in an online search.

I have all LED lighting in my 49 Dodge pickup. I'm on my 2nd pair (turn and hazard) of LED flashers, they are only lasting about a year. The start out well, but slow down to nothing pretty quickly, even noticeable sitting at traffic lights. I'm probably going to end up adding the LED turn assist resisters to my truck.

Those turn signal flashers are bimetal switches. The contacts close when the turn switch is activated, the bimetal heats up and pulls the contact points apart until the bimetal cools and makes contact again. I believe this is done electronically these days, but how that is done is way over my head.