This mosaic came from the floor of a Byzantine Christian Church dateing to the 6th Century CE. It was discovered in Qasr el Lebia, a rural community 50miles west of Cyrene in Libya, and is now displayed in the Qasr Libya Museum. The photo comes from the museum's web site.
The instrument in this mosaic is quite similar to one currently on display in the Metroplitan Museum of Art's Bryzantine Art Collection. The Met’s instrument had a smaller neck, more the size of a ukulele. It is four-stringed and came from Egypt in the 3rd - 4th Century CE.
The Met's web site states, that thier instument, "...is thought to have originated among the West Semites of Syria and was introduced to Egypt as a result of Hyksos influence.” The Hyksos were people from Asia Minor who migrated into Egypt, perhaps through invasion, and even ruled Egypt during the 15th and 16th Centuries, BCE, after which they were expelled by native Egyptian rulers. The Met’s site goes on to say of their little instrument, “Because of its waisted design and its place in music history, this member of the lute family may be considered a possible predecessor to the guitar, in particular the guitarra morisca.”
Clearly, the Qasr Libya mosaic appears to show instrument also has the hourglass shaped body of a guitar. It has four tuning keys, two on top and two below, much in the form of the modern guitar, and not in the form of the European lute or Arabic oud. Arab and native North African Berbers conquered much of Spain beginning in 718 CE, and were the dominant culture for the following 500 years. Based on this evidence, it seems plausible that the Qasr Libya instrument could have made its way to Spain.
Furthermore, there are many African lutes, from ancient Egypt on, which have a round neck, as if a broom handle was stuck through a hand drum. Such a neck can be used to support one or two strings. But the Qasr Libya musician appears to be playing with all four fingers, which would imply that the neck is flat, just like the instrument at the Met.
To me, the Qasr Libya instrument looks like a likely candidate for the origin of the guitar’s neck and tuning peg arrangement, and an influence on the guitars hourglass body shape. If one were to stick this neck on the body of a Roman kithara harp, you could end up with something that looked like a guitar.