People have been fairly open about listing what the non biblical evidence for an HJ is. There seems to be a semantic issue about what constitutes evidence. The word evidence, as I use it, means this: Information that is not known to be false and that if true supports a proposition. Based on that definition of the word, evidence, the list of non-biblical evidence for an HJ is as follows:
1. Testimonium Flavium - My guess is that it an interpolation in total and even it is not an interpolation in total it only provides indirect support for the existence of an HJ since Josephus was not born when the HJ is hypothesized to have lived.
2. Josephus James reference - My guess is that it is an interpolation but if it isn't an interpolation in total it might not refer to the HJ.
3. Tacitus - If true suggests that Christians were in Rome as early as 64 CE. My guess is that there weren't enough Christians in Rome to make the claim that Nero tried to blame the Rome fires on them plausible, but maybe I'm wrong. And Christians in Rome as early as 64 CE provides support for the idea that the origin of Christianity might have dated from the death of the hypothetical HJ in about 33 CE.
4. The fact that people were writing about an HJ by about 100 CE is some evidence that he might have existed in 30 CE.
John Frum shows the fundamental flaw with point 4 and with the Testimonium Flavium, Josephus James reference, and Tacitus even if they were entirely unaltered.
According to the cult, John Frum was a literate white US serviceman that appeared to the village elders in a vision in the 1930s. (Raffaele, Paul "In John They Trust" Smithsonian magazine, February 2006.) However as early as 1949 there were people saying the "origin of the movement or the cause started more than thirty years ago" ie in 1910s (Guiart, Jean (1952) "John Frum Movement in Tanna"
Oceania Vol 22 No 3 pg 165-177)
But the closest thing actual recorded history shows are three illiterate natives taking up the name John Frum and being exiled or thrown into jail for the trouble they stirred up[58]: Manehivi (1940-41), Neloaig (1943, inspired people to build an airstrip), and Iokaeye (1947, preached a new color symbolism) (Guiart, Jean (1952) "John Frum Movement in Tanna"
Oceania Vol 22 No 3 pg 165-177)
John Frum also allows us to see the evolution of the belief.
In 1952 Guiart talks about how the natives would talk of the day when John Frum would come, all the whites would leave, and then John Frum would assume power. This implies in 1952 that the natives didn't see John Frum as a white man.
Worsley's 1957
The Trumpet Shall Sound: A Study of 'Cargo' Cults in Melanesia recorded a new addition to the John Frum story that wasn't around in 1952: "John Frum was King of America, or would send his son to America to seek the King, or his son was coming from America, or his sons were to seek John Frum in America."
Around 1957 John Frum also got himself a brother: Prince Philip, Duke of Edinburgh (who has only sisters) and was being generally being described as a white US service man wearing a white Navy uniform. Some people think that this is due to Tom Beatty a missionary and Navy Seabee stationed in the area during WWII being incorporated into the cult's view and resulted in the lesser known figure of Tom Navy.
By the 1960s people where carrying around photos of people they believed to be John Frum and the three natives who had taken up that name had been effectively wiped from the oral tradition. History seems to indicate that Manehivi if not the founder of the John Frum cult took the idea to a level that it got noticed in 1940 but of him the cult said nothing of other then he was a pretender; for them John Frum was a white US service man wearing a white Navy uniform and some sects have pushed John Frum's appearance all the way back to 1931.
If Jesus did live he may be
nothing like the Gospels describe and may not even be int he time frame the Gospels indicate.
5. Early existence of Jewish Christians. There is pretty good evidence that Jewish Christians existed. There is a story that they were kicked out of the synagogs in 90CE. However, tying the existence of the Jewish Christians that are very likely to have existed to an early circa 30 CE Jesus Palestinian sect doesn't seem to be possible.
6. Josephus mentions John the Baptist. This is generally believed (but not universally) not to have been an interpolation and as such provides a small amount of corroboration for a Gospel story.
7. Talmud and dead sea scroll stuff. I don't see anything here that even qualifies for the highly inclusive davefoc definition of evidence, but there are many things in this world that davefoc doesn't know, so maybe.
There might be some other stuff that some people in this thread would put forth, but this is the list as I understand it. I guess I might have included Suetonius but I didn't feel it.
Nearly all mythic ideas regarding Jesus is the concept predates the 1st century so point 5 is useless. A letter in 1949 states that the spirit of John Frum went back to the 1910's. If the John Frum movement did go back substantially before 1940 no one outside the cult saw it.
Point 6 ignores the idea that to make Jesus important the writers connected him to a more widely known person-John the Baptist.
Point 7 From what I have been shown there is no exclusively New Testament material in the Dead Sea Scrolls and any that has claimed is highly disputed. The Talmud is so late it is questionable as to what it is talking about.