How do you account for the total vaccuum of any contemporary writings from any source,..
It is only a puzzle if you try to view Judea through the lens of the twentieth-century. The Roman Empire was largely a verbal society and information often traveled slowly. The majority of first century inhabitants were illiterate. Also, the well-educated aristocrats who were literate were not always proficient enough to compose documents with the same level of sophistication as we see with Jospehus, Tacitus, or Pliny.
This is how historians infer that Paul of Tarsus was a highly educated and Hellenized Jew. Not only does his philosophy give clues to his upbringing and education, his command of Greek and his penmanship indicate someone who is highly educated and likely comes from an affluent background.
Also, consider that in the first century you could not just run down to Drug Mart and purchase a pad of paper and a pen for a dollar. Not only were writing materials expensive, they were not easy to produce in quantity. The process of putting together papyrus scrolls or parchment from animal skins was time consuming and labor intensive. Most ancient manuscripts were written using the technique of Scriptio Continua: The author created the document using continuous script with no spacing between words or sentences. This saved precious material and money. This is also why scrolls were popular. Creating a codex with individual pages was a total pain in the rear.
Composing documents using the writing implements and material available at the time was also laborious and time consuming. Imagine having to pen just a few small paragraphs on hard parchment or papyrus where you often needed double or triple pen strokes.
In short, if you were going to devote your time and resources to putting something into writing, you had a very good reason to do so. During the life of Jesus, it is doubtful anyone saw anything of significance that would motivate them to devote any ink to what they would likely see as another self-proclaimed prophet who was among the hundreds of others walking the landscape of Judea. It wasn't unit the years following his death, when the stories and legends started circulating, that anyone would likely think it worthwhile to devote any ink to the subject.
That no public historian such as Josephus mentioned anything about Jesus during his life, or immediately after is death, is really not of much value when forming an opinion as to whether the figure of Jesus was historical. It means very little actually.
... and why are the gospels not written in Hebrew?
Hebrew was not a functional language at the time. The use of Hebrew declined following the destruction of Jersualem by the Babylonians. Most Jews found thesmelves dispersed and took on the language of the local society. In Palestine, the use of Hebrew was academic and it was employed for ritualistic purposes. This typically involved the recitation of the scriptures in the ancient tongue. Although many male Jews would have some familairity with the language, this was a very specialized task and typically done by the more learned -- Scribes or Priests. Hardly anyone would have enough of a grasp of the Hebrew language to make functional use ot it.
The majority language of the Empire was Greek, with a large portion of the western Empire speaking Latin. Aramaic was the dominant language for the inhabitants of first-century Palestine.
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