I've never had anything like that happen with any of my GTX-680 video boards. I always used MSI Afterburner for a custom fan curve to make sure my temps stayed under 70°C where the Core Clock would throttle.

Hello!  I am using Open Hardware Monitor with PrecisionX and no overclock set.  I am just using it for the fan curve.  The curve is as follows -
 
Speed/Temp
30/0
30/10
30/20
30/30
45/40
55/50
65/60
75/70
80/80
100/90
 
My temps generally hold around 48-50c when playing Unity type games like Rocket League at max settings.  It's just when idle, no load, the RPMs like to bounce back and forth between 1020 - 1050 or 1050 - 1080 about once per second.  I can hear a soft hum that sounds like an idle up and then back down.  I'm pretty sure it is emitting from the GPU.  Right now, as I type, the fan is at 30% and 30c and the RPM is consistently bouncing between 1020 & 1050.
 
There is a PCI fan that I thought might be causing the issue, so I disabled it.  No go.  I'm new to Nvidia, so it's all kind of greek to me.
 
Should the RPMs hold steady when idle?  

Cool GTX
PrecisionX OC has a fan setting for: 
 
<Click - "Gear icon" (in lower right corner), under "fan tab" of popup box>
 
1) Temperature hysteresis
 
This is the change in temp needed before the fan will change rpm
 
So if it is set to 2, then the temp would have to change by 2C before the rpm would change
 
If it set to 0 (zero) then the fan will wander
 
 
 
2) Fan Speed Update Period
 
Try increasing the time delay (larger number)
 
 
As this is an older GPU, have you cleaned it recently ?

It's pretty clean, but I will give that a try.  I was wondering what the hysteresis function was for.  ;)
 
Thanks everyone.