I'm not sure you could reach those arteries with a push-pin.

The carotid is right under the skin on the sides of the neck. Academically, I suspect you absolutely could reach it with a push pin.

In Jiu Jitsu, you're taught to squeeze on the sides of the neck for a choke. The goal is not to cut off the air supply via the throat so much as the blood supply to the brain via the carotids. Many people pass out in 20-30 seconds of directed relatively gentle pressure on the carotids.

We were recently talking about choke holds in Krav Maga, and it’s shockingly fast when the sides of the neck are squeezed. Within about 5 seconds, for me, I start to get tunnel vision and a profound sense of panic.

That's how they taught us to choke people during basic training in the USMC, and collectively referred to the chokes as "blood chokes" because you cut off blood supply to the brain. It's suprisingly easy to choke someone unconcious just by twisting the sides of their shirt collar, or grabbing someone from behind and squeezing the arteries on their neck with your forearm and bicep. The scariest part about doing it during training is that you don't know that you're about to blackout because you can still breath fine, it's just that none of the oxygen is getting to your brain.

Indeed. I've never lasted more than ~12 seconds, but was being conservative in my response as I don't have any facts on how long it takes.