Go frame-by-frame through a movie with a precise timer

Give Avidemux a try. It should be able to do what you want and is freely available for Windows and Linux.

"Well, seconds are integers. Video players rarely go below them to more precise measurements.

But if you know at what frame you're currently at (which is fairly commonly displayed), and you know the frame rate, you can usually calculate it to much more of a second.
Or you can skip frame by frame while on a time measurement, and the moment the next second ""hits"", switch to frame measurement and then calculate the percent of the next second in which the particular frame occurs.

... just some crazy ideas ... have never had the need for this, so all this is untested ..."

if you don't know the framerate what you also can do is measure the length of the video bar in milimiters, then the length of the duration you want to measure. If you know the total duration of the video then using a simple cross-multiplication you should find out the exact duration you want to know.