This is a common problem with 2006-13 C6s.
This is the fix from another forum.
You will need to remove the bezels, that info
is available if you google it.
Good Day,
I was having the same issue , did a little research on Youtube and came across C&S Corvettes out of Florida who address this specific issue. The link below is the full step by step removal and replacement of the affected switches if you want the proper fix.
Hi Hydroguy. Where are you located? If you are in the Ottawa area, I can come over and show you how to fix this after purchasing the replacement switch online.
There are many workaround, but I chose to actually change the problematic switch. I had purchased 4 of them, but sent 3 to other Corvette owners, after I replaced mine successfully.
Cheers,
Peter