So the intervals, right? Such that you're learning the physical fret distance between the notes and the unique sound quality that relationship has? That is definitely something i struggle with knowing quickly.
Even with the countless hours of practicing I've done over the last few years, even knowing the CAGED system inside out and how to quickly find the root notes based on the shape of the chord and neck position, I still find it really difficult to put all those puzzle pieces together into one whole picture across all six strings and down the neck.
This double stop exercise in thirds you're talking about is really pushing me to expand that understanding of where those puzzle pieces click together. For example, let's say I'm in E and playing the C-shaped E chord with the root at the fifth fret on the B string. I know that 1-3-5 zig zag shape between the B and E string intuitively, also the little triangle 1-3-5 between the B, E, and G strings and likewise I can quickly see/play the 1-3-5 on the A, D, and G strings (with the root at the 7th fret). What I find tricky is, say, playing the root #1 on the B string and then hunting for the third without defaulting to the #3 on the E string at the 4th fret or the #3 but knowing there's another #3 on the D string at the 6th fret. I'm so used to playing those specific arpeggio shapes that it's hard for me to connect those shapes themselves, especially when it involves skipping strings.