I brought the car into an independent mechanic and he came out to listen to it. He said it sounds like a bubbling noise and more likely caused by the aging of the car where the tubes have warped over time and that is it nothing harmful and that I can leave it as is. I didn't take it to a Jaguar service shop where they would probably diagnose it completely and charge an arm and a leg as I believe they would have to dismantle the whole dashboard to get into the one of the tubes just to replace it.

 

Occam's Razor should always be in use...
Asking again if anyone who is hearing this is also experiencing any anomalies with air delivery as per the TSB that was posted a few days ago? I am experiencing both the tick noise and imbalanced air delivery from AC vents. Thank you.

 

I am not even going to out on a limb here, I am going to say its the heater core and it requires changing.
Those are exactly the symptoms I had. I had the gurgling before and after the change though, due to an improper bleed/refill of the system.

I documented my experience on the matter with photos in the forum.