Here's what I've found.
Stock apps (messaging/gmail/missed call) blink the LED. 3rd party apps only have solid LED.
LED color mappings on the GS3 are non-standard. See blog post from Lightflow developer.
Light Flow - Blog
In GoSMS, if I select blue, I get pink, if I select red, I get green.
I just played around with K9 as well, which lets you pick the color. Green got me pink and pink got me orange.
Both GoSMS and K9 also allow you to control blink/not blink. The GS3 keeps the light solid regarding of the app settings.
Either they'll be a GS3 update or the apps are going to have to figure this out slowly and update.
I guess I can use Light Flow to rectify the situation (since I am rooted, which is required for it to function properly on the GS3), but I'm not really sure I want to do that.
I'm a little worried regarding potential Light Flow battery usage and how intrusive (seemingly hooks into a lot of different thing) it could be.
Maybe I'll just get the free version (which doesn't support apps I need it to support) and play around with it for a while and see or just spring for the $2.49 for the paid version.