I am new to speedrunning and livesplit so this might be a noob question, but how are people switching the splits seemingly hands free? usb pedal? secondary person hitting the hot keys?

You mean going to the next split? Most just use a hotkey on a keyboard, I usually put my keyboard in a place so it's closer to my hands and whenever im close to splitting I already move the controller near the keyboard so I can split immediately

When I used to use splits I had a keyboard with all the keys ripped off except the space bar and I put it on the floor so I could split with my foot. Worked like a charm.

my hands are long enough to where I can use the (mostly) unused Pause key on my keyboard for splitting while still being in range of the A button on an NDS or 3DS laying infront of the keyboard. With consoles that's obviously easier, because I'd be holding a controller pretty much 99% of the time, which I can do above a keyboard. I don't really see where the problem is, especially because you may find a closer key that works for you, my setup aims to avoid conflicts with twitch chat being the currently active window.

Not to mention that splits should be planned to happen at a spot with minimal game inputs so you have time to move one hand to your split button for a second. Stuff like loading screens or fade-outs like after a Pokemon battle are optimal for this.

I've known some people to use a foot pedal for it, too.