Butter 8-inch square pan.
Lightly butter inside of heavy, medium saucepan.
Combine eggnog, corn syrup, butter and sugar in prepared saucepan.
Cook over medium heat, stirring constantly, until sugar dissolves and mixture comes to a boil.
Wash down side of pan with pastry brush frequently dipped in hot water to remove sugar crystals.
Add candy thermometer.
Continue to cook until mixture reaches 238°F (soft-ball stage).
Pour into large heatproof bowl.
Cool to lukewarm (about 110°F).
Add vanilla; beat with heavy-duty electric mixer until thick.
Spread in prepared pan.
Score fudge into 36 squares with knife.
Refrigerate until firm.
Cut into squares.
Wrap individual pieces in plastic wrap and decorate with fabric or paper bows.