-
I've had this on nearly every Shimano brifter I've owned. The internals Do seem quite 'wobbly' and once the grease dries out a rattle is inevitable. I've had to pack one of mine with grease again, which solves the problem short term.
A while ago I completely disassembled my dummy lever (tektro / cane creek) to fond out what was causing the annoying rattle. Turned out there was one of those square nuts that are set into a recess down in the bowels of it, that presumably is there functionally when the body is used for a brake, but as a dummy lever it had absolutely no reason to be there.
Originally (2010) I stopped it by spraying a ton of spraymount in there, but it eventually lost it's grip and the rattle had started up again.
I now have a rattle from my left 5800 shift lever :-(
The brake cable-end is located OK.