Are there any instruments or methods which measure the intensity of gray color?
Yes. These measurements are usually performed in the field of colorimetry using instruments called spectrophotometers. Spectrophotometers measure the percentage of light reflected by an object and then the results are used to compute colorimetric coordinates. In the case of grays one could use the Y tristimulus value to look at the relative luminance of the grays or the CIELAB L* parameter (which is a nonlinear transformation of Y) to have a number that correlates better with perceived lightness. All of this can be found in more detail in texts on colorimetry such as Berns’ “Principles of Color Technology, 3rd Ed.
