Isaac stays in Gerar per God’s request. Once the men start asking about his beautiful wife, Rebekah, he pulls a classic straight from Abraham’s playbook:
When the men of that place asked him about his wife, he said, “She is my sister,” because he was afraid to say, “She is my wife.” He thought, “The men of this place might kill me on account of Rebekah, because she is beautiful.” (Gen. 26:6-7)
Isaac, unlike his father, is lying (as opposed to bending the truth). There must be some reason why the Nation of Abraham fears injustice so much in Gerar. If there is, it’s not documented in Genesis. What is documented is Abimelek’s tremendous respect for the institution of marriage (Gen 20:4-5) and his fear of God (Gen. 20:14-16). Why would Isaac doubt Abimelek now?