For modern-day readers of today's Gospel, the sign of Jonah is that he spent three days buried in the belly of the large fish. After three days, the fish spit him alive onto the shore. Thus, Jonah prefigured Jesus' three-day burial and subsequent resurrection.
In today's text, Jesus refers to Jonah being "a sign for the Ninevites" (Lk 11:30). The Old Testament book of Jonah makes no mention of Jonah telling the people of Nineveh about his "fish story." In addition, Jonah despised Nineveh. While he may have enjoyed prophesying their destruction, in his pride he most likely wouldn't have shared his humiliating experience with those he hated. Exactly how, then, was Jonah "a sign for the Ninevites"?
From the standpoint of the Ninevites, Jonah's sign would have been the prophetic words he spoke. To prophesy means simply to speak what God is speaking when He is speaking it. Jonah's timely prophetic words carried the awesome convicting power of Almighty God. The immediate and total repentance of the Ninevites proved the power of prophecy.
Your words may be eloquent, but God's prophetic words have the power. "The time is short" (1 Cor 7:29). Let's spend the rest of our lives (1 Pt 4:2) speaking God's words, not ours. His words spoken at the proper time change hearts (1 Thes 2:13; Heb 4:12-13). "Set your hearts on...the gift of prophecy" (1 Cor 14:1).