It could simply be the gpu fans. Those are relatively small fans that spin relatively fast, and depending on design can produce some funky harmonics. I know I personally am not a fan (no pun intended) of the Gigabyte cards, not from a performance standpoint, but solely due to the pitch of the hum those fans generate.
Also figure that fans are a moving object that creates sound. Sound is an oscillating frequency, it vibrates, and can transmit that to anything else that's not sufficiently dampened or secured. Meaning if a rivet is the tinyest bit loose, the metal framing it attaches can rub and create a high pitched squeak that sounds very similar to coil whine. That's easier to diagnose by flexing the case corners, which puts torque stress on the frame. If the sound changes, you have a vibration somewhere. If it doesn't, it's more than likely gpu coil whine and only changing the cards voltage/load might change that.
Checking the case fans is a good idea, but I'd not recommend using your fingers, far too easy to damage the fan that way. Instead use bios or FanXpert or SpeedFan etc to isolate the individual fans and either turn them full blast or shut them down. If it is a fan, the sound will change with the speeds.
You can do similar tests with the cpu and gpu, using stress testers like furmark and Prime95, as those will drive the individual components to extreme highs, while leaving everything else running minimally.
Coil whine is loudest at one specific frequency, not the whole band, so will be evident if it disappears in a gpu stress test.