The Sons of the Forest Action Cam is a new item that was added with the latest update. It can be found inside a bunker on the east side of the island, though you'll need to make sure you're prepared with weapons and guns unless you're playing in Peaceful mode, as there are a few enemies to deal with along the way.
A flashlight will also come in handy inside the bunker, and you will need the Guest keycard to access the area where the Action Cam resides. Depending on where you've got your base set up, it might be quite a trek to get to the bunker in question, so make sure you've got a good supply of food and water before you set out. With that in mind, here's where to find the Sons of the Forest Action Cam.
Sons of the Forest Action Cam location
The Action Cam is found to the east of the large lake on the eastern side of the cannibal-infested island. I've marked the exact location of the entrance in the screenshot above. Once inside, follow the linear path until you drop down into the bunker itself and follow the corridor down the stairs until you reach the double doors. You'll need the Guest keycard to unlock these doors and proceed from this point.
Follow the corridor beyond to a red door, and a cutscene will play. Once it's over and you're In the next room, head past the plants on your right, then go through the single doorway at the end and into another long room. Keep heading forward, and you'll eventually reach a stairway on your left.
Follow these stairs until you reach a door with the number two next to it. Go through two more long rooms and two more doors, then take a left down more stairs. Follow these down quite a way until you reach a door labelled five. Follow this corridor, then—finally—take the door on your left, just before the door at the end. You'll find the Action Cam on a cabinet, just in front of a red radio. Good job!