Highlight Perfect Forward Secrecy
Perfect Forward Secrecy (see https://www.eff.org/deeplinks/2013/08/pushing-perfect-forward-secrecy-important-web-privacy-protection) provides better protection to users than traditional SSL encryption by preventing communications from being decrypted en masse.
However, very few sites use this. Google might be the only large provider at the moment and Facebook may be considering it.
I suggest that a styling be applied to the HTTPS Everywhere icon, or some other indication be provided, to highlight sites that use this. Making users aware that there are gradients in HTTPS security and highlighting those agencies that are doing it right fits well with the cause of this program.