I watched the video and it does appear that your temperature gauge isn't working properly.
I believe that once you're at I/O mode #25, the indication is supposed to be at 00 as you saw and stay there (if it says err, it's definitely broken).
Then it's supposed to go to H, stay there for two seconds, the go to Center for two seconds, then cold for two then back to hot.
Then it says ( fixed ) which I believe means it stays fixed in the hot position. ??
Your gauge gets pinned past hot and stays there...
It looks like it is trying to go to cold but only goes to the hot line, then back to pinned.
I don't believe the temperature input signal has anything to do with the test mode... It should behave as described regardless of engine temperature.