Caprice no. 13 at a glance appears to be a study in the octave, and my first instinct was to play the octaves with the modern approach of 1st and 4th finger (ie: lots of shifting). With further study, I realized this was the wrong approach: the work also explores arpeggios, tenths, and other intervals. Furthermore, if Campagnoli wants a fingering that takes you out of first position, he will usually indicate it.
Therefore, most of this caprice stays in first position. Ironically, staying in first position makes intonation more difficult. This is because often, you jump from the C string to the D string, or the G to the A, and the left hand has to adjust across the fingerboard. So, in order to play this successfully, your left arm will have to swivel slightly, back and forth to guide the LH adjustment. You can see how this works for me in the video.