Oh, border collie! I thought "Big Cock" and was confused. Why would you acronyze "border collie" when there isn't even any context that you're talking about a dog?

Maybe you could search youtube for "driving ASMR" to find videos of driving with good audio, and then look for oen that has turn signal sounds somewhere in it.

We have a very nervous border collie as well. She was pretty sensitive to a lot of things especially when she was young. But exposure and her getting older helped with it. You could probably just google turn signal sound effect and there'll be ones not on YouTube.

Our border collies are pretty good in the car but we also use a very secure harness so they don't get to walk around in the back seat. Seems to help keep them relaxed as well because they fall asleep all the time. Also recommend crate training especially if your dog tends to damage things when bored.

We had this with other sounds. Finding a similar sound might not work because they have better hearing than us. Record the turn signal sound with a voice recorder app on your phone. Then play it to the dog but in a safe place for the dog and at very low volume. So low there is no reaction at all. We had to start so low that I couldn't hear it. Play sound, mark and reward, repeat.

Try to keep sessions short and fun, gradually increase the volume. Don't try to go too fast or you'll just have to start over.

You probably can't with a turn signal but see of you can turn it off or down. Most cars these days it's not a real sound and is just played through the speakers so there might be a volume setting somewhere. Our dog was also terrified of the beeps the washing machine made when it finished. Would run off to hide under our bed, surprisingly it had volume settings in the manual and i could turn it off completely.