... but it isn't hitting anything. I wager the bearings are giving up slowly. It's a 12G-P5-3967-KR.
 
My card is still under warranty, but since it still "works" I don't think this is a RMA case.
Could somebody please advise me if replacement fans for this are available for purchase? At least once my warranty expires, I'd have fan replacements to put in myself.
 
Any help greatly appreciated.

I would agree that it’s best to contact EVGA and see if they have a replacement fan. Depending on comfort level it might be something you could do yourself or the option to send it in would also exist. I would definitely recommend taking advantage of thenwarranty if it’s still under it and contact EVGA since you don’t want to have a clicking fan and no warranty.

I have contacted EVGA and they were super quick and willing to send me a replacement for free, which is awesome.
 
What turned out is that my card at times of low load would cycle back and forth between 0-fan and running, within seconds, and the fans do emit a low clicking sound when they turn off or start back up. The constant repetition of it was annoying.
 
Then it turned out as well that a different fan in my system is making noise under load, so I conflated things.
 
The solution in the end is to take care of the fan that's noisy under load (a case fan), and to switch my card to the "OC" mode where the fans will always run so I am rid of the 0-fan/start-fan wobble.
 
They were excellent, I love EVGA support. I so much hope that they will make video cards again some day.
 
Thanks all!