I went to my local Sprint store during my lunch hour to discuss this issue with them. They were not even aware that ICS was released for the E4GT yet.
When I explained the problem (LED notifications for GMail and SMS, not for any other email), they took it to the back to have a tech work on it. Forty-five minutes later, the tech could not figure out the problem. She said she tried to reflash the phone multiple times and the phone would not accept a flash! She also thought the email applicaiton was messed up because all it would show is "Refreshing...". This wasn't a problem before because I was receiving email messages just fine, just no LED notification.
What she finally did was replace my phone with a refurbished unit flashed with EL29. She told me that once the notification arrives to update the OS to ICS, proceed with the update and come back to the store if the LED problem reappears.
Needless to say, I am not a happy camper as I don't believe there was anything wrong with my original phone. I still feel that ICS was not properly debugged prior to being released to us, and here it is 7 months after it was first released to the world.
To be honest, if given the option, I'd switch my E4GT to a Nexus.