Mnemonic-led: Casal's necklace equals pellagra equals the 4 Ds, and pellagra is caused by deficiency of Niacin (vitamin B3) plus its precursor tryptophan. The necklace itself is the photosensitive hyperpigmented dermatitis that rings the neck where sunlight strikes, so the answer is niacin.
Eliminate fast. Vitamin A loss gives ocular signs, night blindness, Bitot spots and xerophthalmia, not a neck rash. Iron loss gives microcytic hypochromic anaemia with spoon nails. Vitamin B12 loss gives megaloblastic anaemia with neurological deficits. Only niacin deficiency produces the dermatitis, diarrhoea and dementia triad with Casal's necklace, more often in women because estrogen metabolites inhibit tryptophan conversion.
Ref: DM Vasudevan, Textbook of Biochemistry, 6th edition, pg 395.