To trigger an output, the player must be in the volume, and looking at the entity in the "look target" box.

I've provided an example map, because it's easier than explaining it in detail. Just make sure you learn something from it.

If he won't... I will!

Create a trigger look that sets the value of a info_branch, named player_is_looking to the value of 1.

The trick is in changing this back 0 when the player is no longer looking. If the trigger_look does not automatically refire once it is triggered then you could kill the brush and respawn another with a point_template.

i.e A trigger_look is in place, when a player is looking at the area the trigger sets the logic_branch to one, then kills itself, then spawns another of itself, and resets a timer which if left to run, will set the logic_branch back to 0.

I can make an example if this isn't making any sense to you.

The trigger_look is capable of what you are asking, although this feature seems to be undocumented on the wiki.

Firstly, you need to uncheck "fire once" in the flags, and check "clients". Now, the part that is undocumented is the fact that, when fire once is not checked, the "timeout" value resets the triger, and cancels any pending outputs. So, to give an example, a light (let's call it "red_light") that comes on when you look at the correct place:

"Look target" to the object you want to look at (obviously)
"Look time" to "0", so the triggering is instant
"Field of view" to "0.0" (which equates to 90 degrees, change this as needed)
"Timeout" to 0.5 (again, change to suit. Ignore the description, when used in this manner it is the refire rate of the trigger)

Now, for the outputs:
OnTrigger>>Target "red_light">>via input"Turn On">>delay "0"
OnTrigger>>Target "red_light">>via input"Turn Off">>delay "0.6"

Now, as you can see, the light is set to turn back off after 0.6 seconds. However, this doesn't happen, since the trigger resets itself and refires after 0.5 seconds. If you aren't looking in the right direction at that time, the sequence is allowed to complete, and the light turns off.

I'm not sure how taxing it is to the game to have the trigger performing in this manner, but it works okay in testing. I'll attach the vmf. I used a light so you would be able to see it's effect even when you aren't directly looking at it, but i see no reason why it wouldn't work with other entities.