Compare the videos and you'll find that Eddie isn't the fastest or the hottest in that style, which is unusual for Eddie. But it had a funk that made it interesting, at least for the Van Hagar-era.
(Just as a point: I'm a big fan of pre-
Back to the topic at hand, I found this article in Guitar Player. GP is, by content, my fave guitar mag, and with their online articles, they're even cooler. But here, it kinda fell down. Some of the notes in chicken pickin' are muted to death. We know that. It gets the name because three muted notes followed by a snappy one are supposed to sound like "bk-bk-bk-Bgak!" Like a chicken. But there's something missing here. Something that takes a simple use of this style, going bt-ting-bt-ting-bt-ting and moves it closer to what we hear on those two YouTube videos.
Here's the first thing. Pull-offs and the use of your bad mother finger. (I'm going to have to use that line more and more.) Unlike Greg Koch (and like Guitar Tube, I think) I grab the string with the fleshy part of my finger. I can't get the snap with my fingernail. Adding to that the knowledge that country guitar tends to use pentatonic major, and you can pull-off chromatically. So, that's helping.
Here's the second thing. "Memphis Soul Stew". Doesn't the "Finish" lick sound so close to the "Soul Stew" lick? Eddie thinks he's playing country, but really, he's playing soul! The technique here is to play the outlines of chords with a few high strings. "Soul Stew" and I think "Finish" are across the D and B strings, while the lead parts to "Soul Man" are on the G and E strings. My first knowledge of this style and of it's roots came from a commentary on Jimi Hendrix's version of "Like A Rolling Stone" from Monterey Pop. I forget where I read it, but it said that this is really from his chitlins circuit days.
So, I know how to get the pop. I know how to get the thud. I kinda know how to get the speed. All I need know is substantial practice and fretboard knowledge. That looks like a plan, eh?