References: 

• Comedian Bill Engval had as a part of his routine a joke about stupid questions. “Here’s your sign,” was an “I’m stupid” sign.
• The word for sign in Greek is σημεῖον (say-mi'-on)
  • A common word used 77 times in 69 vss in NT
  • It can be positive
    • signs and wonders accompanying those sent by God (Acts 5:12).
    • Circumcision was a sign that Abraham already had faith and was accepted by God (Rom 4:11)
  • It can be negative
    • Judas gave a sign for his betrayal of Jesus (Mt 26:48)
    • The religious leaders demanded a sign (Luke 11:29-30)
• The sign for the shepherds was a baby, swaddled and lying in a manger.
  • While there is no Biblical evidence for it, there is rabbinic tradition that describes a practice of swaddling lambs marked for sacrifice …
    • Protection: Wrapping lambs in cloths (swaddling) prevented them from getting blemishes, ensuring their suitability for sacrifice, and a manger offered a safe space.
    • Symbolic Significance: Bethlehem was known for its temple lambs, and shepherds would recognize swaddled lambs in mangers, making the sign in Luke 2:12 meaningful for them as representing the "Lamb of God".
  • No room in the κατάλυμα (kat-al'-oo-mah)
    • Mark 14:14; Luke 22:11
    • Guest room not inn
      • An inn is πανδοχεῖον (pan-dokk-i'-on)
      • Luke 10:30-37 (esp. vs 34)
  • Jesus was found in a common, peasant home where the shepherds would have been welcome and at home, not concerned for his safety or well being. (Compare Matthew 2:11)
  • The sign was one to honor and lift up the lowly. So, they rejoiced and praised God (vs 20).