This is working great for me.

https://www.amazon.com/BK01-Bluetooth-Hands-Free-Wireless-Streaming/dp/B01MSUWCZ0/

I've got an iOttie car mount and the Besign BK01 Bluetooth adapter, it turns on with my car and turns off, works like a charm!

This bad boy works great for me. I have an older model (2007) so the aux and 12V power ports might be in a different location. But the cord measurements are listed. https://www.amazon.com/BK01-Bluetooth-Hands-Free-Wireless-Streaming/dp/B01MSUWCZ0/

I would recommend something like this. It has a ground noise isolator so you won't get alternator whine (super annoying, basically it plays your cars RPM in a whine out of your speakers)

I have a 2nd gen. I bought this in December and haven’t had any real issues. Most of the time it auto turns on and connects, but some times I just have to press the button to turn it on. The USB part is connected to the usb in the upper glove compartment and the wires are pretty well contained. I mounted the “puck” between the air flow selector and the volume button.

Get this and plug it into your USB in the upper glove compartment just for power. That way your 12v outlet in the center remains free for... activities.

Edit. Sorry. Didn’t read your aux port is acting up. This... doesn’t help...

If you have a little bit of patience and know how, and can follow directions, then the installation won’t be too hard. To keep the steering wheel controls, you’d need to adapt the signal to the aftermarket stereo with a kit like this one:

https://www.crutchfield.com/p_541RP4VW11/PAC-RP4-VW11-Wiring-Interface.html

Additionally, Crutchfield (linked above) is a good resource if you haven’t heard of them as they provide fitment information and instructions.

Finally, as an alternate, simple solution, this is what I used for my 07 Jetta as it made it easy to run the wire inside the glovebox and still access the bluetooth module: https://www.amazon.com/BK01-Bluetooth-Hands-Free-Wireless-Streaming/dp/B01MSUWCZ0