It’s just such a lazy trope for creating some drama out of nothing, by “fooling” the loyal viewer.
Checking the pulse at the neck in period dramas
They go to all this trouble to get all the right stuff, but can’t get the basic first aid right.
Just watched Poirot on TV – same thing.
The policeman checks to see if he is dead by putting his fingers on the neck.
In the 1940s! – No way.
It would always have been to feel the wrist.