I emailed BBTS for an update. Here is their reply:
"Thank you for bringing this to our attention! After reaching out to our Product Department, it appears that we will be receiving these figures in wave shipments and do not anticipate fulfilling all preorders until quarter 1 of 2018...
Try flipping the batteries in the neck post so that the negative side is closer to the switch. The directions show the positive side up, but I flipped the batteries in mine and now the light function works.
Up for pre-order at BBTS -
Regular: https://www.bigbadtoystore.com/Product/VariationDetails/62287
Deluxe: https://www.bigbadtoystore.com/Product/VariationDetails/62284