Why is λόγος accusative singular in John 19:8 and genitive plural in John 19:13? In both cases λόγος is the object of the verb ἀκούω (hear). There seems to be three possibilities.
In v8 Pilate believed the statement v7; in v13 he did not believe the statements in v12.
There is one statement in v8 and two statements in v13.
In v8 Pilate had no intention of following to their reasoning to condemn Jesus in v7 while in v13 Pilate was inclined to give in to their reasoning based on the statements in v12.
The Jews answered him, “We have a law, and according to that law he ought to die because he has made himself the Son of God.” 8 When Pilate heard this statement [τὸν λόγον], he was even more afraid. 9 He entered his headquarters again and said to Jesus, “Where are you from?” But Jesus gave him no answer. (John 19:7–9, ESV)
12 From then on Pilate sought to release him, but the Jews cried out, “If you release this man, you are not Caesar’s friend. Everyone who makes himself a king opposes Caesar.” 13 So when Pilate heard these words [τῶν λόγων], he brought Jesus out and sat down on the judgment seat at a place called The Stone Pavement, and in Aramaic Gabbatha. (John 19:12–13, ESV)
Abbott supports option 3 in his grammar.
 19:8 ὅτε οὖν ἤκουσεν ὁ Π. τοῦτον τὸν λόγον μᾶλλον ἐφοβήθη may be compared with 19:13 ὁ οὖν Π., ἀκούσας τῶν λόγων τούτων ἤγαγεν ἕξω τὸν Ἰ. In the former, the “hearing” does not produce (1614 b) any result beyond emotion; and the clause, being subordinate in thought, is introduced with a subordinate conjunction. In the latter, τούτων is emphasized by position (2553 c) and τ. λόγων τούτων by case (1614 b)—referring to the words “thou art not Cæsar’s friend.” This is a charge that Pilate cannot hear unmoved. Now therefore he is goaded to action, and the sentence introduces the action as the consequence, ὁ οὖν Π … ἤγαγεν. -- Abbott, E. A. (1906). Johannine Grammar (p. 435). London: Adam and Charles Black.
Abbott apparently took this meaning from this classical use since τῶν λόγων τούτων the the things hear, not the people speaking.
ἀκούω ... IV. to listen to, give ear to, Il. 2. to obey, c. gen., or more rarely c. dat., Ib. 3. to hear and understand, κλύοντες οὐκ ἤκουον Aesch. -- Liddell, H. G. (1996). A lexicon: Abridged from Liddell and Scott’s Greek-English lexicon (p. 29). Oak Harbor, WA: Logos Research Systems, Inc.