And if you agree the writers didn't make up the words of Jesus than it would be reasonable to conclude that the writers (2 of which, Matthew and John, were eyewitnesses) didn't make up their account of the resurrection.
Evidence for the bolded bit?
Well here is some of the evidence that the eyewitness Matthew was the likely author of the Gospel of Matthew.
From the site "Gospel of Matthew"
1.2.2. There are other early sources that also claim that Matthew wrote a gospel in Hebrew or Aramaic.
A. Irenaeus (130-200) (Adv. Haer. 3.1.1; also quoted by Eusebius, H.E. 5.8.2): "Now Matthew brought forth among the Hebrews a written gospel in their language, while Peter and Paul were preaching in Rome and founding the church." By “Hebrews” Irenaeus probably meant Palestinian Jews. The language that Jews in Palestine would have spoken was Aramaic, although many Jews had a literary knowledge of Hebrew.
B. Origen (185-254) (as quoted by Eusebius, H.E. 6. 25.3-4) asserts, "Among the four Gospels, which are the only indisputable ones in the Church of God under heaven, I have learned by tradition that the first was written by Matthew, who was once a tax collector, but afterwards an apostle of Jesus Christ, and it was prepared for the converts from Judaism, and published in the Hebrew [or Aramaic] language."
C. There is a tradition cited by Eusebius, alleged to have originated with a man named Pantaenos (died c. 190), who was associated with the church in Alexandria, that there once existed a Gospel of Matthew written “in Hebrew letters” (H.E. 5.10.1-4): “One of these was Pantaenos, and it is said that he went to the Indians, and the tradition is that he found there among some of those there who had known Christ the Gospel of Matthew had preceded his coming; for Bartholomew, one of the apostles, had preached to them and had left the writing of Matthew in Hebrew letters, which was preserved until the time mentioned” (see H.E. 3.24.5-6). According to Jerome, Pantaenos brought back a copy of this Hebrew version of Matthew to Alexandria (De vir. ill. 36).
D. Eusebius reports the view current in his time is that Matthew's gospel was based on his preaching to Palestinian Jews, whose first language no doubt would have been Aramaic. Naturally, Matthew's gospel would have been written in Aramaic. He writes, "For Matthew, who had at first preached to the Hebrews, when he was about to go to other peoples, committed his Gospel to writing in his native tongue, and thus compensated those whom he was obliged to leave for the loss of his presence" (H.E. 3.24.6).
E. Jerome (342-420) more than once asserts that Matthew wrote his gospel in Hebrew, and says that it is not known with certainty who translated it into Greek. He even claims that the original Hebrew gospel can be found in the library at Caesarea (De vir. ill. 3; see Ad Damas. 20; Ad Hedib. 4). Jerome sometimes refers to this Hebrew Gospel of Matthew in order to clarify the meaning of the Greek text.
F. In describing the Jewish Christian sect known as the Nazarenes, Epiphanius (315-403) writes, "They have the Gospel according to Matthew quite complete in Hebrew, for this Gospel is certainly still preserved among them as it was first written, in Hebrew letters" (Panarion 29.9.4). It seems that he is referring to the same Hebrew version of Matthew known to Jerome.
http://www.abu.nb.ca/Courses/NTIntro/Matt.htm
And if the Gospel is true it really doesn't matter who wrote it. I've already pointed out 5 of the 10 reasons given in the Geisler book as to why we should believe that the NT authors told the truth.
I'll get to the Gospel of the eyewitness John as time permits.
