Well, I figured it out, and I want to contribute to the forum, even if I am answering my own question.
But first, thanks to all who offered advice.
And second, it will make me feel better to publicly state that the customer service offered by Villa International, who made the captain's chair, is completely non existent. I emailed them and called them about my question, and they could not even extend the courtesy of responding. Thanks for nothing Villa!
To reconnect power to the seat, remove the seat pedastal (6 bolts). At the rear of the bottom cushion, stuffed up towards the seat back, are two bundles of wires, each secured with a large wire nut. One bundle is mostly red wires, and the other bundle is mostly black wires. I am not at all convinced that this location is where the original "pigtail" originated, but I connected power there and the seat works.