I was searching for something totally unrelated and by sheer coincidence I discovered this — did you know that, in the times of Saul, Arabia was the region (including Kingdom of Nabataea) right at the eastern border of Judea? Nabataea was annexed by Trajan in 106 AD and became known as the province of Arabia. Some maps indicate that, in the time of Jesus and Saul, Damascus was located on or at least very close to that eastern border of Roman Empire with what was known as Arabia at that time. Makes me wonder whether Saul, for the time being, simply escaped to the nearest region outside of Roman and Jewish priestly jurisdiction as opposed to travelling all the way down to current-day SA and Yemen for a pretty speculative reason.

Maps:

• Roman provinces 31 BCE — 14 CE (Augustus)
• Roman provinces in 125 CE (Hadrian)
• Roman provinces around 400 CE