Again, that it was no new god which recommended by Christ, was clearly attested by the opinion of all men, because some maintained to Herod that Jesus was the Christ; others, that He was John; some, that He was Elias; and others, that He was one of the old prophets. Now, whosoever of all these He might have been, He certainly was not raised up for the purpose of announcing another god after His resurrection.
But nothing can be inferred, from Tertullian's words, about Herod concluding:
Ἰωάνην ἐγὼ ἀπεκεφάλισα
The only reason Klinghardt puts this connection "Herod as killer/John" in his reconstruction is that:
In the Lukan version, on the other hand, Ἰωάνην ἐγὼ ἀπεκεφάλισα constitues a problematic narrative void, since it does not provide the corresponding account about the death of John the Baptist. This suggests that the remark Ἰωάνην ἐγὼ ἀπεκεφάλισα was cointained already in *Ev. Mark adopted it, supplemented it with the added narrative...
(The Oldest Gospel and the Formation of the Canonical Gospel, p. 705, my bold)
I don't like this explanation, sincerely. It is a mere suggestion, not a proof, of the presence of Herod killer of John in Marcion.
Hence I am justified to think that in the Evangelion Herod was surely informed about the various identities of Jesus according to hearsay, but he never concluded: "I have beheaded John".
The corollary is that the original readers of Marcion would have assumed that Pilate had beheaded John the Baptist, not Herod.