Look on Amazon for those magnetic cell phone holders. You can get ones that are suctioned to the dash (what I use) or ones that clip to the vents, or even ones that are glued to the dash. The brand names vary.
I picked that style because I saw a foreign rally driver using one to record his runs, and his phone stayed attached through a brutal off-road stage.
The magnet mount might work if it can work for a rally car. I'll be driving this thing hard and want something secure but also look like it belongs. Here is what I use on my Rx8. The windshield mount is for track days and road trips. The other ram mount goes in what would eventually become the passenger airbag shutoff key hole. Looking for ideas as I'm sure some of you have figured this out.
(Sorry for the terrible lighting)
So, what I did is junkyard an extra vent surround trim piece (so I can put it back to stock). Then I very carefully drilled a hole in my "extra" (while it was off the car of course). I started with small drill bits and then slowly widened the hole until it fit the bolt that I wanted. The bolt I used is the standard size for camera tripod mounts. I can't remember what that is off the top of my head. I was planning to just surround it with a big old blob of hot glue but, (IIRC) it actually wedged in place just fine. Then I took the beefiest magnetic tripod-mountable phone/tablet holder I could find (https://www.amazon.com/ORASANT-Magnetic-Horizontal-Rotatable-Anti-Wobble/dp/B07GVBF2GX) and threaded it onto the bolt with a nut to try and keep it in place. If I had to do it over again, I'd probably use a slightly longer bolt.
So, this was all about 2 years ago. The bolt has stayed in place just fine and there's no sign of the vent surround cracking or anything. The phone holder itself definitely holds my phone just fine, but I think the plastic ball joint in it is starting to wear out a bit because it wants to rotate a bit. Not that annoying really, I just straighten it out once in a while.