Was Gamaliel a believer?

“Because of his sympathetic attitude to the early Christians, at an early date Christian ecclesiastical tradition has supposed that Gamaliel I embraced the Christian faith, and remained a member of the Sanhedrin for the purpose of secretly helping his fellow-Christians (compare Recognitions of Clement I.65,66). According to Photius, he was baptized by St. Peter and St. John, together with his son and with Nicodemus. His body was said to be preserved at Pisa, in Italy. Contemporary Jewish records, however, continue to list him first among the Sanhedrin; this would be highly unlikely if he had been a convert to Christianity.” —Wikipedia

“The Jewish accounts make him die a Pharisee, and state that: “When he died, the honour of the Torah (the law) ceased, and purity and piety became extinct.” At an early date, ecclesiastical tradition has supposed that Gamaliel embraced the Christian Faith, and remained a member of the Sanhedrin for the purpose of helping secretly his fellow-Christians (cf. Recognitions of Clement, I, lxv, lxvi). According to Photius, he was baptized by St. Peter and St. John, together with his son and with Nicodemus. His body, miraculously discovered in the fifth century, is said to be preserved at Pisa, in Italy.” —Catholic Encyclopedia

“As a consequence of being mentioned in the New Testament, Gamaliel has become a subject of Christian legends (Schürer, “Geschichte,” ii. 365, note- 47). A German monk of the twelfth century calls the Talmud a “commentary of Gamaliel’s on the Old Testament,” Gamaliel is, here plainly the representative of the old Jewish scribes (Bacher, “Die Jüdische Bibelexegese,” in Winter and Wünsche, “Jüdische Literatur,” ii. 294). Even Galen was identified with the Gamaliel living at the time of the Second Temple (Steinschneider, “Hebr. Uebers.” p. 401). This may be due to the fact that the last; patriarch by the name of Gamaliel was also known as a physician (see Gamaliel VI.).” —Jewish Encyclopedia