When you resolve “Beckoning Light”, first discard, then pick cards to add to your hand. So you can add cards to your hand that you discarded while resolving “Beckoning Light”.
If you don’t have enough LIGHT monsters as there are cards in your hand, you cannot activate “Beckoning Light”.
You cannot activate “Beckoning Light” if you have no cards in your hand.
If your opponent chains “Disappear” to “Beckoning Light”, and there are no longer enough LIGHT monsters to retrieve as there were cards in your hand, the effect of “Beckoning Light” disappears and you don’t discard your hand or add cards to your hand.