I think we could have tested anything for temporal dithering a long time ago. But it is expensive: Lossless capture card, be it internal or external, and a fast PC. I don't have neither. If anyone is willing to spend a lot of money, those 2 requirements are the keys to prove dithering once and for all.
The software needed to check if individual frames of a captured lossless video are the same or not most probably already exists. Just extracting some frames of a losslessly recorded desktop video where nothing moves and saving them as lossless images should be possible with many video applications, maybe even command line tools. Then running any checksum utility on them should be enough to prove the images changed. And then you could use Gimp/Photoshop to determine what exactly changed.
Of course a custom-made all-in-one application that does all of this automatically would be more convenient, but I believe it is not needed.
Edit: Maybe it is not that expensive at all: https://www.elgato.com/en/gaming/game-capture-hd60-s
I read that 175 € USB 3.0 card can send uncompressed video via DirectShow. It does 4:2:2 chroma subsampling, but that probably wouldn't affect temporal dithering's visibility. @JTL?