I doubt you are using the right hardware. A webcam uses USB bus power. You would need to build a switchmode or similar power supply with different rails (voltages)

I guess it costs nothing to experiment, I am not super au fait with power supply design but you can often find designs on electronic forums (this one is more consumer level) - basically a couple of LM-317 s or 350's with appropriate added-on bits.

I would think a cheap reversing camera which you can buy in auto stores would be better, they will include mounting hardware then you will only need to supply 12v unless they have a 24v option built-in.

To work out the supply voltage of the camcorder screen (are you sure the screen works) ideally you want to measure the voltage supplied along the flexible cable, and go from there.

Don't forget a webcam will not have a 'video out' but a digital signal. That's going to be muy complicated. I would suggest a cheap security camera, which will come with a housing and mounting hardware. You can get them in most electronics stores or online, and they usually take 12v, some ac or dc.

The webcam would be too complicated.

Can a USB webcam be attached to a video picture frame?
A little searching on the internet would tell you that.
Got me interested now.

My power chair is also 24volt. It's just two 12volt batteries
in series. You could easily tap 12volt off just one of the batteries.

Pooh Bear