Note: Yellow connectors and harness wrapped in yellow wire loom should not be probed. These are SRS wires for the airbags.
In the radio harness (at the back of the radio), there is a GRN/RED wire. This is your steering wheel remote input wire.
Right past your steering wheel adjustment lever, there should be a gray 4-pin connector. This is for the audio controls, more specifically the GRN/RED wire in it.
The next connector in the circuit is near the main relay and near the driver side fuse panel under the dash, it's a blue 22-pin connector. Look for the GRN/RED wire again.
Basically, with the radio on, you can perform a voltage drop test between these points to find a break or short. First, measure battery voltage between the terminals to determine your baseline voltage, around 12.6V on a healthy battery. Use your multimeter leads to probe the wire at one connector and another. A difference (or drop) in voltage of more than 0.50V (from the baseline) will indicate extra resistance in the circuit. No voltage tells you there is an open in the circuit between those two points. Measuring the same points and getting infinite or an OL reading for resistance also indicates an open in the circuit.
My guess is that the contacts in the clock spring are worn out or the resistors in the steering wheel controls are burned out. The switch operates by using a set of resistors in the switch to change the resistance in the GRN/RED wire and the radio reads the resistance as a command to adjust volume or seek up. At the switch itself, there are two wires, GRN and BLK. I don't know which is power or ground (you'd think black). If one of the wires shows power, you know that the wiring up to the switch is fine and that the control itself is the problem. If there's no power at the controls, check power before the clock spring. If there is power before the clock spring, but not after it, you know the clock spring is bad and needs replacing.