If I signed an authorization card, do I have to vote in favor of the union if an election takes place?

No. If the union collects enough cards, there will be no election and there will be no vote. Then your signature on the authorization card is your vote for the union. But if the union does not get enough cards, and there is an election, you may vote your opinion as of the date of the election. You are not bound to vote for the union on the basis of your signature.