I have an old packet trick called "Now is the Hour" and it sounds exactly like the one that you have described. I bought this probably over twenty years ago and it really played well for a lay audience. The instructions are labeled as "Another Quality Product from MURRAY's MAGIC & NOVELTY" of Willoughby, Ohio. No credit for the effect is given but it would be good to know who this belongs to....
The effect, as written in the instructions, is thus:
The hours of a clock provide a thrilling and colorful triple surprise. Introduced is a wallet containing a prediction card, and a pack of 25 cards with 25 different back designs. Assistant visualizes the face of a clock and mnentally selects any hour. Assistant takes one card from the pack for every hour mentally selected (this is done while magician's back is turned). Magician lays 12 cards on the table in the pattern of a clock. Assistant reveals the hour mentally selected, takes the card at the mentally selected hour and places it in the center of the clock pattern. The prediction card is removed from the wallet and layed next to the selected card. The back of the selected card and prediction card match (these are the only two cards with matching backs) The two cards are turned face up; the faces also match (example: 3 of hearts) Assistant turns face up all the remaining face down cards. Each and every card is seen to be the same (example: King of Spades), but different than the assistant's selected card and prediction card. The cards the assistant removed (1 card for each hour mentally selected) are now revealed and turned face up. They are also King of Spades. The only two cards that match back and face are the selected and predicted cards.