The exact meaning of invoke can depend upon its context. For example:
"invoking God's help"; or "invoking the spirit of the dead" — to call upon a great or magical power
"I invoke the First Amendment"; or "I invoke the words of Thomas Jefferson" — to cite or call upon for validation
"She invoked his sympathy and family memories." — to call upon someone's feelings or memories
"She invoked his assistance." — to call earnestly for
"The program invokes the subroutine" — to call up a computer program
He used all his money for a ticket, boarded the train as he had done many times, coolly chatted with the conductor, to whom Dill was a familiar sight, but he had not the nerve to invoke the rule on small children traveling a distance alone if you've lost your money the conductor will lend you enough for dinner and your father will pay him back at the end of the line.
invoke = call upon
There are no more uses of "invoke" in To Kill a Mockingbird.