Evidence that Peter (and Paul) were Martyred in Rome

Evidence that Peter (and Paul) were martyred. Moreover, that the place of martyrdom was in Rome: - 1 Clement claims that both were martyred, and given that Clement lived in Rome, his description may imply that the martyrdoms took place in Rome. He may have even been in a position to know this first-hand. (95 A.D.) - John 21:18 clearly implies that Peter was martyred by crucifixion (80 - 95 A.D.) - Ignatius’s letter to the Romans seems to imply that the martyrdoms took place in Rome (110 A.D., possibly later) - 2 Timothy, which has the strongest support of the pastorals of being authentic (given the style of language and undesigned coincidence of the metalworker, see here), implies that Paul is imprisoned in Rome and approaching his death, or at the very least reflects an early tradition of Paul’s martyrdom in Rome. (65 A.D.) - 1 Peter 5:13 probably refers to Peter’s presence in Rome, whether or not this letter is authentic or merely reflecting an early tradition. (65 A.D. - 85 A.D.) - Apocryphal literature, such as the Acts of Peter and the Acts of Paul, clearly refers to Peter’s crucifixion in Rome and Paul’s martyrdom there. (160 - 180 A.D.) - Gaius mentions a “trophy” in Rome for Peter. (190 A.D.) - Archaeological evidence in the Vatican Necropolis corroborates these traditions. (100-180? A.D.) - No competing traditions exist that Peter or Paul died elsewhere. Given the later primacy disputes and later church emphasis on apostolic pedigrees, the location of the martyrdom of the two most important apostles would be a badge any church would desire - yet no claimants other than Rome exist. The importance of this point is hard to overstate. Clement’s evidence has more weight than at first sight. As F.F. Bruce points out, Clement’s language of the “great multitude gathered around” the apostles echoes Tacitus’s language about the Nero persecutions, in which he speaks of a "great multitude" killed by Nero. Clement is most probably referring to the deaths of the apostles in Rome. Some of the points may be elaborations on the same stream of attestation, and thus may not represent a true independent witness for the martyrdoms.

In any case, I'm collecting all of this to argue for these two points, specifically point 2, which tends to be neglected at the expense of point 1: 1. There were eyewitnesses who claimed to see Jesus resurrected physically and his tomb empty. 2. These same eye-witnesses were willing to die for this belief.