How to shake/wobble camera on movement?(3D First Person),How to add a small wobble or shake to my camera when walking(3D First Person)

I'm making a horror, exploration kinda game, and right now, my movement feels smooth, like too smooth.

I want it to look a bit like this https://www.youtube.com/watch?v=r6NCC-nnvMU Notice how the camera "shakes" as the player walks?

I tried calling a function that changes the rotation of the camera in the z-axis every set interval, it ended up looking really weird, I played around with the values a lot before I decided to scrap it. Next, I tried animating the camera, but that didn't look much different either.

Looking back at other similar first-person games, they all seem to have some form of subtle shake as the player moves, maybe not one as apparent as the one PT had.

Any suggestions/help would be much appreciated, I've been stuck on this for a while now. Solutions using scripting methods would be ideal cause I'm really bad with animations and stuff like that.