Since the comments ask for a more complete answer from me, I'm going to give it a shot.
Most people I know call this technique double stops.
In the case of Soul Man, the double stops are mostly based on a 6th interval, starting with a (sorta) outline of an E7: |-----4----2-2----7---9---11---12-| |---------------------------------| |---2/4--4/2
-2--/7---/9-
-/11
--/13-| |---------------------------------|
|---------------------------------| |---------------------------------| Another way to use double stops is to slide around inversions of diatonic chords based on the root, 3rd and appropriate 7th interval.
A good example of this is the song 3rd Rate Romance by The Amazing Rhythm Aces .
I'm horrible with this jTab thing and tab in general, which I why I answered in a comment.
:)
You can check here for a more complete example that even covers a bit of Soul Man.
:)
A google search for "double stops" also turns up a fair amount of material.
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He's just picking there in a country style; Dont know if there is a specific name for the technique:
As Follows (Assuming this is the bit you mean ): $4.15 $4.17h $2.20 $4.17 $2.18 $4.17 $2.16 $4.17 $3.19 $4.17 $3.17 $4.17 $3.15 $4.17 $3.14 $4.15 $4.17 Note this doesn't go up and down the neck but is essentially the same thing; the root G is often muted in the track.
Actually from the timbre of the bit in that track he's probably starting the run on the G string at the 12th fret.
Pattern's slightly different from there
but im
sure you'll figure it out.
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I think the technique you are looking for is a double stop (although, I don't really hear it on the Beck piece, it's on the others).
A double stop, generally, is playing two notes together at the same time.
However, double stops are used a lot in blues with a rather distinctive sound.
The double stop tends to be V - I or I - III, although when using them heavily in a solo, you could certainly use other intervals (like the 6th suggested by JimR in a comment).
A search for "double stop blues" on google will give you a bunch of lessons and example licks.
The following isn't actually a lick, but it's a series of double stops that I would use regularly over a blues solo in A.
The first two are A, the third one is the E, and the fourth and fifth one are the D, these can be used over the chord changes, picking up the grace not (D#) as you progress from V - IV.
$B.5.$e.5 $G.9.$B.10 $G.9.$B.8 $G.7.$B.6 $G.7.$B.5 $G.14.$B.13 $B.17.$e.15 $B.17.$e.17
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It's called chicken picken.
You use your fingers/nails to pick the string very hard causing it to slap against the neck similar to slap bass guitar.
The type of run he is doing is using intervals descending down the neck.
He's not doing exact chicken picken
but it sounds like a hybrid between normal and chicken.
Generally when you do this you alternate with a thumb or pick attack that is muted and then the hard attack with the fingers giving a very characteristic sound.
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Eddie VH does something similar with "Finish What You Started", which in context of the song he clearly associates with a country chicken-pickin' kind of thing, but to my ears connects to the soul thing.
I'd strongly suggest King Curtis and "Memphis Soul Stew", where Cornell Dupree pulls it out.
Another good example of these R&B double stop licks is Jimi's take on "Like A Rolling Stone" at Monterey Pop.
The part that really connects to is how for many of the notes, the pop and rhythm of it is much more important than the actual note played, but it's more a part of what you might hear a hot country picker play in a lead context, while in the Isley, Curtis and Sam&Dave context they're more a popout lick in a rhythm guitar context.
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Jeff Beck plays variations of this blues lick - 1:28 into "You Know What I Mean" - It's a basic blues riff (the beginning to Dust My Broom (Elmore James) played with variations up/down the fretboard using the G and E string -  What the heck is this technique called?
The intro to "Soul Man" - the verses in "It's Your Thing" (Isley Brothers) - What is that technique called?
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A double stop, generally, is playing two notes together at the same time. You use your fingers/nails to pick the string very hard causing it to slap against the neck similar to slap bass guitar. The technique is known as playing double stops or chicken pickin'.
Double stops. Chicken pickin'