When history isn't clear, it can be advanced in the same way science is advanced when conclusive evidence through experimentation cannot be obtained.
Historians formulate theories about the subject. Then they try to support their theories by finding corroborating evidence. Given theory A then X, Y and Z must have existed. Then Historians go out into the field and try to find archeological evidence for X, Y and Z. If enough corroborating evidence can be found and a convincing case assembled, it is presented to historical committees made up of respected experts of the period and they judge the voracity of the case. Sometimes the originators of a theory are not the ones who transform the theory into accepted history. Sometimes that is done decades, even centuries, later with the help of facts or science unavailable to the original historian.
As such the search for Arthur goes beyond just trying to uncover new historical texts. Every time archeologists discover previously unknown fortifications, and evidence of advanced commerce at sites associated with Arthur, knowledge of the mirky period in Britain's history progresses, and light is shed on Arthur. The ruins at Tintagel and Chester are such examples.
National Geographic (August 2016)
A recent discovery in southwest England is making headlines for its association with King Arthur, but archaeologists are hailing it as an incredibly important find regardless of any connection with Britain's greatest legendary ruler.
Excavations at Tintagel, a rocky promontory on the coast of Cornwall, have revealed evidence of massive stone fortifications and luxury goods imported from as far away as modern-day Turkey, all dating to a poorly understood period in British history that began with the collapse of Roman rule on the island around 400 A.D.
According to 12th century historian Geoffrey (of Monmouth's Historia Regum Britannie- "History of the Kings of Britain"), Arthur was conceived at Tintagel after his father, Uther Pendragon, disguised himself (with the help of Merlin) as a local ruler and slept with the ruler's wife.
The Telegraph July 11, 2010
Historians locate King Arthur's Round Table
Historians claim to have finally located the site of King Arthur’s Round Table – and believe it could have seated 1,000 people.
Researchers exploring the legend of Britain’s most famous Knight believe his stronghold of Camelot was built on the site of a recently discovered Roman amphitheatre in Chester.
Legend has it that his Knights would gather before battle at a round table where they would receive instructions from their King.
But rather than it being a piece of furniture, historians believe it would have been a vast wood and stone structure which would have allowed more than 1,000 of his followers to gather.
Historians believe regional noblemen would have sat in the front row of a circular meeting place, with lower ranked subjects on stone benches grouped around the outside.
They claim rather than Camelot being a purpose built castle, it would have been housed in a structure already built and left over by the Romans.
Some of the theories compiled around Arthur are truly fantastic. Take the ongoing quest for the Holy Grail which legend has it was found by the Arthurian knight Sir Galahad, and according to one amateur historian recently rediscovered, in a loft in Rugby.
the Independent August 10, 1995
One man's quest for the Holy Grail ends in a loft in Rugby
An amateur historian claims to have tracked down the sacred relic after years of research.
The extraordinary find came to light after seven years of investigations by a Coventry-based historical researcher, Dr Graham Phillips, who tracked the potential "relic" down to a house in Rugby, Warwickshire, where its owner kept it in a box in the loft.
Dr Phillips has unearthed a substantial body of evidence linking the find - a small green onyx cup of possible Roman date - to the Grail legend.
In the medieval Arthurian romances, the Holy Grail was the cup used by the man who buried Jesus - Joseph of Arimathea - to collect Christ's blood. However, the origin of the medieval legend appears to have been a real historical grail "found' in the 4th century AD by the newly-christianized Roman imperial authorities who turned it into a sacred relic.
According to the 5th century Greek historian, Olympiodorus, this original Holy Grail had been used by Mary Magdalene to collect Christ's blood and was found by the Christian Roman empress, Helena, inside Christ's Holy Sepulcher.
Saint Helena, or Constantine the Great's mother, who also found according to Roman and early Catholic sources the cross which Jesus was crucified upon. Constantine the Great ordered the Church of the Holy Sepulcher, built upon the site where his mother found said cross.
Constantine appointed his mother Helena as Augusta Imperatrix, and gave her unlimited access to the imperial treasury in order to locate the relics of Judeo-Christian tradition. In 326-28 Helena undertook a trip to the Holy Places in Palestine. According to Eusebius of Caesarea (260/265 – 339/340), who records the details of her pilgrimage to Palestine and other eastern provinces, she was responsible for the construction or beautification of two churches, the Church of the Nativity, Bethlehem, and the Church of Eleona on the Mount of Olives, sites of Christ's birth and ascension, respectively. Local founding legend attributes to Helena's orders the construction of a church in Egypt to identify the Burning Bush of Sinai. The chapel at Saint Catherine's Monastery—often referred to as the Chapel of Saint Helen—is dated to the year AD 330.