To understand resistor noise, I recommend reading Chapter 12 of
https://pearl-hifi.com/06_Lit_Archive/14_Books_Tech_Papers/Motchenbacher_Connelly/Low-noise_Electronic_Design.pdf , which is an update of the classic monograph by Motchenbacher and Fitchen: "Low-Noise Electronic Design", Wiley 1973.
I'm not aware of any equipment from that era specifically designed for measuring excess noise in resistors, but the books discuss test equipment designed to measure noise of amplifiers and semiconductors.
The fundamental difficulty is that the excess noise only rises above the unavoidable thermal noise in a resistor at relatively low frequencies, where measurements take a long time.
In some semiconductor devices, the "corner" frequency where excess noise exceeds thermal noise is much higher.
A recent technical article on measuring resistor noise:
https://www.mdpi.com/1424-8220/23/3/1107It includes a good review of measurement techniques since 1960.
The reasonable ones for experimentation use Wheatstone bridges (presumably with three known good resistors) and a spectrum analysis, which could be done possibly with a good sound card after a preamplifier.
Remember that excess noise only appears with substantial voltage applied to the resistor, while thermal noise is always present at a finite temperature.
Back in graduate school, I measured excess noise in thick-film high-voltage resistors by
very carefully applying 300 V from a dry battery (no longer available) and coupling the output through a good capacitor to a low-noise current preamplifier (from Princeton Applied Research, no longer available) into a strip-chart recorder. One must be very careful not to smoke the input of such a preamplifier with spikes from applying the voltage.