I forgot to mention that as one of the many things I tried. In fact, I deleted the "FTBHorizonsII" folder so that the launcher would re-download and re-install the modpack. After downloading/installing a second time I ended up with the same result.
So now I started on a layman's process of trying to see if one of the upgraded or added mods is the culprit. My plan is to start with a 1.0.2 install and then graft onto that the added and updated mods found in 1.1.0. So, I deleted the FTBHorizonsII folder, ran the launcher, downloaded and installed the 1.0.2 version, created a new world with it, and NEI worked as normal. I exited and renamed that folder to "1.0.2 FTBHorizonsII". I ran the launcher, downloaded and installed the 1.1.0 version, created a new world, and NEI had the greyed out tabs. I exited and renamed that folder to "1.1.0 FTBHorizonsII". I renamed the "1.0.2 FTBHorizonsII" folder back to the default name. I added the five mods added to 1.1.0 (as per
http://www.feed-the-beast.com/modpacks/FTBHorizonsII/changelog), copying the mods right from the "1.1.0 FTBHorizonsII" folder. I ran the launcher, changed the mod pack version to 1.0.2, and launched my world. NEI worked fine. Exited, then updated the mods as per that link five at a time, relaunched my world, tested NEI. I am up to mods that begin with the letter "D". So far, NEI is working fine.