So I've been playing for a few hours and have gone as far as The Hub.
I've noticed, all this time, that no matter how many times I right click the weapon icon during combat, I never get the target symbol which signifies a targeted shot.
I've gone through several different pistols, and my small guns skill is around the 90% range. I should also have enough AP to fire a targeted shot - but the option just never comes up. Instead, I cycle through Fire Weapon and Reload.
Anyone have any ideas why this would be the case?

Weclock is right. I had the same problem in one of my earlier games, and I think that was it.

Yep, Weclock is totally right. I hadn't realized Fast Shot made it impossible to use targetted shots.
To restart, or not to restart. That is the question.

I restarted about 5 times after downloading the game.. :)

Ouch. I thought I had, but I mustn't have read the whole description. XD

You can use the Mutate perk, I believe, and change Fast Shot to something else.

Restart. Fast shot is a pretty negative trait later in the game, when gun skills are high and eye shots are epic, and Mutate wastes a perk.