Actually, there is a very clear way to tell when you are done shocking the pool. The way to tell when you are done is if you add bleach at night to raise your FC, and in the morning it has stayed high and not dropped to near-zero. Sunlight breaks down chlorine but starlight and moonlight don't.
In other words, your FC can drop during the day due totally to sunlight's UV rays breaking it down. But nighttime, if your FC falls, you are fighting something. So if FC stays up, or doesn't drop too much, you've killed what ever you are fighting. At that point you can think about adding stabilizer.

As Watermom says, it's sold as Stabilizer, Conditioner, or Cyanuric Acid. You don't have to use stabilized chlorine.

Carl