No. A video of you sitting in front of your computer screen not touching your mouse or keyboard would not prove that:

you did not set up a program to move the mouse all over the screen

you were not playing back a video of an earlier session you had run

you hadn't given someone else remote access to your machine, even in the same room

the screen wasn't connected to a different computer being run by someone else

A video might be influential in reaching a conclusion but it wouldn't be conclusive by itself. In the same way, you could disconnect internet access to your machine and record that the "aberrant" inputs only occur when the computer is connected to the internet or that the input stops when the connection breaks. That again would make it more likely but you wouldn't know. It could be that someone has installed hardware in your machine, or in your mouse of keyboard, that allows it to receive signals even with the internet off.

However, a smart person would have set up that hardware so that any control it has cuts off when your are not connected to the internet unless they really feel the need to do something and override that cutoff.

But a smart person wouldn't have let you notice so it doesn't seem like that it was a smart person so you don't have to worry about that trojan horse hardware.

But a really, really smart person would know that you'd know only a less smart person would be found out so they let you find out so you think they're less smart than they really are.

You can try putting packet sniffers on your computer to analyse where the data reaching your computer are coming from but like I said, the hardware could be compromised and bypassing the internet and even if it wasn't you'd have to trust that the person allegedly controlling you computer hadn't hacked that software.

To be sure that no one has compromised your computer all you can do really is throw it away and then you'll have no computer for anyone to remotely operate.