I am both a car enthusiast and audiophile and have seen this question posted a few times elsewhere as well.
First off, forget the GoPro built in audio its OK at best but on any thing moving at speed is going to be mainly wind noise and some engine crackle in the background.
The shotgun you have will do just fine and all you really need to do is capture the audio in a static situation (unless you want audio of the car passing buy). The way I would go about this is to shoot the video and patch in some dummy audio of the engine after the fact. FWIW it will much easier to capture the engine noise with the car not moving and you will get the tone you are looking for. An engine revved up while parked is pretty similar to when its under load. In this case you can use any mic you like, a condenser, small or large diaphragm will work as will the range of popular dynamics. Cars have a pretty high SPL output so you don't need something super sensitive. You should keep in mind (although this is a newer car) exhaust is a dirty thing and you should keep the mic out of the direct line of the tailpipe as well as the spray of gasses that come out.
Im not sure why you would put a mic in the engine bay and I would not for a few reasons.
- Its extremely hot in there and you can damage the element
- There is not a ton of noise in there on modern cars, you will hear some valve tapping and lots of air moving around
Most of the audio you want is going to come out of the tailpipe and thats where I would focus my efforts. The key is to try and record on a day with not a lot of wind so you can reduce issues from it. Since you are just going for audio you can chose a day that may not be great for video recording.
I have owned and driven a wide variety of cars and frankly the movie car audio you often hear is a poor representation of what engines really sound like. the vast majority of cars dont make some fancy air compression release noise when they shift (fast and the furious). Cars dont shift 25 times in a 1/4 mile drag race.
To get good in-motion audio you will need a chase car (something quiet, an electric if you can get it). You will have a wind issue but you can get a variety of wind screens for this which may help. I have tried this a few times and never gotten a solid result so I wont offer much more than that.
This is a great documentary that has some great audio of car engines. Magnus is a very nice guy and if you reach out to him may offer some advice on how he captured such good audio of his cars.