Saying someone is “like a deer in the headlights” implies they are both vulnerable and unable to act. As noted on quora, “there’s a (generally illegal) form of deer hunting known as “deer jacking” that exploits this reflex of the deer. The jackers go out in the dark and shine a bright light at deer to get them to freeze, making them much easier targets.” It seems that deer really do this.

This is an American phrase and the British, according to phrases, have their own version: caught like a hare in the headlights. This seems odd because, while I’ve seen rabbits zig and zag in front of a car (what works to escape a coyote doesn’t work as well with a car) I’ve never seen one freeze as the car approached.

While I didn’t find the first citation, word-detective says:

‘to look like a deer in the headlights’ leaped into the public vernacular in a big way with the 1988 Presidential campaign of George H.W. Bush and his running mate, Senator James Danforth (“Dan”) Quayle. Quayle’s reaction to [an attack during a debate] was described the next day by several commentators as like a deer in the headlights, frozen in fear…

A deer-less relative of the phrase appeared in print more than a decade earlier:

‘It is only when they commit some offence that they are caught in the headlights of history,’ Daily Telegraph, 1971), although this usage seems to reflect the sense of ‘came to public attention’ rather than ‘caught clueless.’