While there isn't a way to do this as you've asked the question, there is a simple way to do it.
If I'm correctly interpreting what you're after here, you have a display connected to computer A, receiving a signal from it. You want to connect up a cable from computer B to the same display and see what is shown on the display from computer A. No, this isn't the way displays generally work, at least not without some fairly heavy customization.
This is actually a fairly common ask for people that work with video. What we need to do it split the video signal coming from computer A before it gets to the display so we can get a copy of it on computer B. Easy peasy.
In between computer A and the display, we put a video splitter. One side of the splitter feeds the display as usual, the other side goes to a video capture card in computer B and we capture any video that we care to.
Additionally, building a splitter into a display would not be an onerous task. We'd likely want an older display, so there was a little space in the housing to work with, but it could be done.
On the positive side
- This would be very difficult to detect without physically eyeballing the hardware
- Its a relatively simple setup that we can put together with off the shelf components and software
- Gaining access to log on to the target system itself would not be required, as all the components on that side are hardware
On the negative side
- Visually inspecting the hardware would turn this up almost immediately, unless we buried the hardware in the display housing -- even then there would be an extra cable leading to another (extra?) system nearby
- Running video captures for any period of time would result in huge output files -- you couldn't reasonably leave it on all the time
More than likely, you would be better served with something like a keystroke logger, presuming you could get on the system in question.