If necessary it is possible to create a profile that captures the behavior of a separate display as you are doing. Since the calibration program would not be run on the same screen as the one you are profiling, you’ll need something else to run it - like a laptop. Then you will need a way to display the colored PNGs on the in-car display, and time them accurately. Often times that’s the tricky part.
This is similar to how we created a profile of the first iPhone.
MeasureTool is a free download from the X-Rite site which is part of the ProfileMaker suite of tools. For calibrating displays they offer a 99-patch series of colors for LCD’s and a 42-patch target intended for CRT’s. That gives you an idea of the range of how many colors that would be expected, although your infotainment display is probably closer to an LCD and thus might require the larger number of colors in order to capture the spiky behavior of these displays. You can also create your own color lists for MeasureTool to use. Other software allows this too, I think ColorEyes Pro.