Either connecting to separate inputs on your monitor, separate monitors (a bit extreme), or getting a VGA switch box that can switch one display between two sources is what you want. A passthrough is simpler but it's kind of disappointing just how much this degrades image quality on the desktop. Especially at 1024x768 or higher. I'm not sure if some cards have clearer pass-through than others, but any that I have seen left a lot to be desired. Seems crazy for how expensive these were back in the day. Also, by avoiding the passthrough, you will know 100% for sure which device is generating the image. The downside is that games that switch often between 2D and 3D (for example, to show a menu versus being in game) will require manual switching... only the card's passthrough will do this automatically unless you get some kind of automatic switch box but I doubt those work as well in this situation.
EDIT: Something like this would probably work:
Data Sharing Device DW-HD15AB VGA Manual Transfer Switch Box DE-15
VGA Manual Data Switch Box
Or an old KVM switch, though ideally you want something that isn't seen as a display device itself... you want something that is completely passive, yet shielded enough to not make things worse.
Last edited by Stiletto on 2020-03-02, 06:12. Edited 1 time in total.
Reason: removed eBay links
Now for some blitting from the back buffer.