It seems to predominantly be in G mixolydian. Or is it mixodorian? Well I play G maj with the flat 7th (F) whatever that is. Straight maj (F#) works also but as usual cohesion is everything. It would be best to start out in G maj pentatonic.
Heavy emphasis on the chord notes for F (F, A, C) and C (C, E, G) when playing over those chords. Chromatics especially transitioning between chords, i.e. from G to C, and from G to F then C back to G.
Jerry would add the flat 3rd (A#) strategically placed to start getting a little nasty. This would sometimes lead to some G minor or G blues pentatonic chromatics. In short Jerry would draw from a broad spectrum of approaches and wittle it into a cohesive, stampeding herd of cattle. I'll try to tab some examples soon.