When you say "ticking noise" is it in time with the strobe portion firing, or constant?
When they ran the new power cables from the dash panel switch, are they bundled with audio wiring at any point in the harness where the wires are virtually in contact with each other?
Continuous DC loads create a nice consistent continuous magnetic field around the wire.
Pulsing DC loads may look like AC on the "bounce" as the light pulsing circuitry turns the new "strobes" on and off. They induce pulses in wires near them. If you had the old Nav lights and flipped the switch on and off rapidly, you might hear the same sound.
Audio is AC. "Coupling" between audio cabling and a cable that used to carry a continuous DC load (nav lights or a power source to a traditional strobe flash circuit out in the wing away from all the audio circuits), that is now a pulsed load, may now be happening behind your panel.
You may need to re-route the "strobe" power circuit away from any audio wiring.
Also check the run from under the panel to the wingtip... does it run behind an audio jack or other audio system input or output? Tie-wrapped to a cable coming out of a radio?
If they must physically cross, cross them at a fixed 90 degree angle. Parallel will couple the most noise from one to the other.
Try to isolate whether the noise is coming in through a specific input or output on the audio panel. See if it continues if the audio panel is switched off and in fail safe mode hooked to Com 1 only. If not, select the Crew isolate switch and see if it gets better or stays the same. See if having headsets in all jacks makes it worse or better. Try deselecting everything on the audio panel while leaving it powered, and see if it's still there.
With that testing you may find a mode or input that's worst. Suspect the cabling from that radio, or input is strapped to the power cable somewhere and start tracing.
Does your headset cord position change it? If yes, suspect the power cable run is right where your headset cord hangs, behind a thin piece of sidewall plastic and carpet. Also suspect that the inputs to the audio panel may have RF bypass capacitors that are dried out and leaking, or we're blown in a past "event". (Or on a cheap audio panel, never existed.)
If you can figure out if it's coming from cable "cross-talk" an appropriate ferrite bead of the right material may be used as an RF choke on the wire to block or subdue the induced voltage. Re-routing is better.
If the strobes are just hideously noisy at RF frequencies and inducing oscillation in the audio panel's amplifiers, a better case/frame ground of the audio panel itself may help if it's in a metal case.
A handheld oscilloscope and knowledge of how to use it might be employed "listening" to various cables.
Or even a simple lineman's "butt set" for a high impedance amplified audio speaker to probe around and see which wires its travelling on. In on-hook mode, don't close the loop with off-hook.
There is significant chance you can short out the DC bias going to the headset jacks. A good audio panel won't care. Others you might damage. Caution advised.
There's about a billion things to check. Lots of labor. Lots of shops just "shotgun" in a filter somewhere, hoping for the best. Without finding root-cause.
Newer Cessnas have single point bus grounding and home-run grounds back to it. Older Cessnas have ground-loop problems because the aircraft structure is used as a ground.
