Equip Spell Cards can only be equipped to face-up monsters. Even if the Equip Spell Card increases the DEF of the monster, like "Horn of Light", you cannot equip it to a face-down monster. You need to wait until the monster is face-up on the field.
Equip Spell Cards only have their effect as long as they remain face-up on the field. If an Equip Spell Card is destroyed or is removed from the field in another way, then its effects disappear.
Usually, if a monster equipped with an Equip Spell Card is destroyed, returned to your hand, shuffled into your Deck, sent to the Graveyard, turned into an Equip Spell Card (by "Relinquished"), flipped face-down, or anything else so that it is no longer a face-up Monster Card on the field, all Equip Spell Cards equipped to it are destroyed.
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