So, I was having a similar issue, back in December when I got my card. Under high usage gaming, the card was totally stable no issues whatsoever even with a heavy overclock. However, on the desktop under little to no-load, or in non-demanding games, I would get black screen crashes, sometimes the card would recover, and sometimes it would totally lock up the pc. I looked around and couldn't find a solution. The issue made no sense to me, the only reason I could think of is that there is something in the bios of the card or the driver for the card that causes the GPU to dip to unsustainable voltages when the card was downclocking for power savings under a light load. So, I changed the global power management mode in the Nvidia control panel from "Normal" to "Prefer maximum performance" and I haven't had a single black screen or crash since, and it's been almost three months now. It's not an ideal fix, as the GPU doesn't underclock under low load for power savings anymore, but it sure beats the hell out of the card dying all the time on me.
I don't know if anyone else has suggested this for those of you who are still having black screen issues in light gaming, and I apologize if someone has, but I figured I would mention my experience in the hopes that it might help one of you until Nvidia or Evga issues a proper fix for the issues.