Discussion Forum—A Way with Words, a fun radio show and podcast about language

That's an interesting Ngram you cite. What immediately came to my mind was a reference to: registering a deflection of the indicator/pointer/needle on some analog measuring device. So when used as a metaphor, it would mean simply "registering a response" or "causing a response."

Analog measuring devices for barometric pressure, electrical voltage and current, and probably many other uses date back to the 18th century. At first, that was probably the only meaning to "move the needle." I have no idea when it entered the language as the metaphor I described. When I looked at some of the passages cited around that spike in usage between 1860 and 1880, they were all about scientific instruments (including magnetic compasses).

This is just an educated guess, but the 1860-1880 spike itself could be because that era was a time of prolific scientific invention. Also, the telegraph was coming into widespread use about that time, and the original telegraphs used "deflecting needles" instead of "clicking solenoids."

Of course, it's use as a metaphor will soon become an anachronism as more and more analog displays are replaced by digital displays. But I don't expect that the metaphor will be replaced by something like "advancing the digits" ... it just wouldn't have the same emotional impact.