How did the king of Gerar discover Isaac was lying about Rebekah?

Answer: He saw Isaac caress her

Abimelech looked down from a window and saw Isaac caressing his wife Rebekah.

“When Isaac had been there a long time, Abimelech king of the Philistines looked down from the window and was surprised to see Isaac caressing his wife Rebekah.”— Genesis 26:8 (BSB)