Lost trip and climate control after JVC install

Here's a post with the information, but for a Gen 3 liftback. It will at least show you what to look for in your own model's electrical wiring diagram.

You'll see that the buttons work completely differently depending on whether the car does or doesn't have Touch Tracer. That was an option in the liftback. I don't know if it was ever a thing in the v.

 

My TIS subscription is lapsed most of the time until I have specific things I want to look up, so I can't easily pull up your 2012 v wiring diagram right now, but that is what I would suggest for you to do (more info) to get the least-likely-to-be-wrong info.

The EWD includes the circuit diagrams (like you saw in that linked post), and also drawings and descriptions of each connector and which wire goes to which pin, and also "location and routing" drawings that will show exactly where in the car each involved connector is found. The electronic version is interactive and will highlight all the components, wires, and connectors in a circuit that you click on, and let you easily jump between those views.

You sometimes have to pay rather close attention to the asterisks (as you saw in that linked post) because the diagram can include variant circuits for different trim levels and you need to make sure which variant is yours.