From the NASA website about Perseverance, the rover has two microphones on board. Can it use both microphones at the same time to pinpoint the direction a sound is coming from? Has this already been done? If not, why not?
Perhaps the mics have different characteristics (e.g. they have different frequency ranges) that make it impossible to do this?
If:
...then the answer should be yes, even with just one mic.
For short sounds, you would need a "stereo mic" (like ears in human and animals), but probably you could determine direction with +/-180° approximation (you need to rotate your head to precisely determine the location of a sound source).
But probably kind of a calibration would be needed in advance, to know how the microphone(s) react to sounds from different locations. But such calibration could be performed only for EDL microphone, because the only "controllable external sound source" around Perseverance is the laser impact on rock, which unfortunately always comes from the same direction from supercam microphone point of view.
I have no idea about the specific reasons for the behavior of this rover, but it could be as simple as, how loud is Mars? If the rover often makes more noise than anything else nearby, maybe it just can't hear anything else clearly enough to locate it. I don't know either way, but it's worth considering: how loud are the signals of interest, and how loud is the noise (the sum of everything else)? Cross-correlation signal processing can provide significant gain, but only if the signal has enough structure of the right kind.
The primary explanatory Wikipedia article I would recommend is Multilateration, or, as we call it where I work, Time Difference of Arrival (TDOA) geolocation. It is closely related to the things (ILD, IPD, and ITD) mentioned in the articles @uhoh linked, but rather than trying to exactly match what animals do, this is the method usually used in computer processing of both radio and sound signals for navigation, so it's what I would assume JPL's engineers would choose.
If the sound you're locating lasts long enough, you can just move the microphones relative to each other to generate new TDOA surfaces. The source of the sound is located wherever all the surfaces intersect. Animals do the same thing in order to hear more precisely: they turn their heads to get new baselines, and some twist their ears to change where their antenna patterns peak. Since Perseverance has one ear fixed to its body and one on the end of its boom, it could generate the effect of having three ears by extending, retracting, or swinging the boom around; but only if the noise being located lasts long enough, and if they wouldn't cause too much disruption to the missions of all the other sensors sharing the boom by moving it like that.
