I was experimenting using very short shutter times today with the A7. At exposure times shorter than about 1/2000 second, a gradient begins to appear at the top of the frame, becoming quite strong by 1/6400 and 1/8000 second. Turning off the Electronic First Curtain Shutter option eliminates it.
Based on what I know about how EFCS works, I'm pretty sure this is just a characteristic limitation of the EFCS implementation on this camera. Does anyone else have thoughts about it?