Nick, my apologies, as I didn't realize the 2012 Equus apparently doesn't support Bluetooth Audio. I also didn't realize there wasn't a Home button where all audio sources are listed, as on my 2016.
And the reason you are probably having the rapid vibrating sensation with your phone could be the cable you are using to connect it to your car. A typical lightning-to-USB cable will not work with this system. You must use the genuine Hyundai iPod Cable (Part # 08620 2L000) which
plugs in to both the USB and audio inputs of your Equus and ends in a 30-pin Apple connector. I've seen these anywhere from $5 to $30 on Ebay and other sources.
If your iPhone is newer than an iPhone 4s, you'll also need a genuine Apple 30-pin to Lightning adapter. It is important to get an actual Apple adapter which retail for $39 but can be found much cheaper from other online sources.
Once you have both cables, plug them together, then plug the lightning end in to your iPhone and the other end in to your Equus. Now select AUX. You should now be connected and hear the audio through the Equus sound system.
This worked for me on my 2009 Genesis with what appears to be the same audio system and user interface using my iPhone 6s running iOS 9.3.5. It "should" work with other newer iPhones but I can't verify that as I no longer have the Genesis and have not updated my iPhone to iOS 10 or iOS 11.
Here are a few links for the two cables you'll need:
https://www.ebay.com/itm/New-HYUNDA...ash=item213642d965:g:J2sAAOSw88xaTO6N&vxp=mtr
https://www.apple.com/shop/product/...f79d4f3cece89e85c15db0fe3d2960060c92aa3d8e6d8
If you still have issues even after all of this, there is one more way to do this by using a stereo cable from your iPhone's headphone jack to the stereo input jack on the Equus. (If you have an iPhone 7 or newer, you'll need to use the supplied lightning-to-headphone adapter.) Select AUX. You'll have to control all functions and overall volume output level from the iPhone itself when doing it this way but it will get the job done. Also, be aware that your iPhone will not charge when connected this way.
I'm hopeful the first solution with the two adapters aforementioned will work just fine for you. Let me know how it goes! Brent