Okay, I tried it again at the lowest moving RPM I could get, and I got a lag effect like what you showed in the video. At anything higher than idle, though, the response is almost instant (i.e. 0.37 seconds in my video above).
I also decided to do a little more in-depth analysis of your original video. In the first stock run, the time between hitting the pedal and the first visible tach movement is 0.63 seconds. With the cable unplugged, this time is reduced to 0.47 seconds, a difference of 0.16 seconds. Out of curiosity, I also measured the time between initial tach movement and 2,000 RPM, and the results were 1.2 seconds stock and 1.07 seconds unplugged, a difference of 0.13 seconds.