They've prototyped displays that can test for it as well.
As I recall (it's been many years; likely over a decade since I saw it) he tested it with a woman who was believed to have tetrachromatic vision. She could reliably tell the difference.
As a control, he tested it with a man who was trained as a graphic artist.
He too could reliably tell the difference.
That result strongly implied the test did not work as expected.
Do you know anything about this previous work? I tried reading the paper but was immediately out of my depth.
But we'd need a convenient way to sample a 4D space of colors (perhaps with 4 monochromatic sources?), and thereby generate different spectra that normal trichromats see as the same color (called "metamers"), but that tetrachromats could recognize as distinct. And, how the 4D space is sampled would have to be pretty carefully optimized to generate distinct spectra that have the same response with the M (medium or "green") and L (long or "red") cones (which are actually quite similar already!) while also generating different responses for the putative tetrachromat's additional code between M and L. And that isn't possible with any conventional display device.
It's not very uncommon for people to be colour blind, dichromats. If media on screens would be dichromatic while the world around me is trichromatic, I would certainly notice at once.