The call was initiated by one of the newfangled "interactive" robocallers that pretends to be a human. It, subsequently, passed me to a live agent who, after I requested their address, hung up. He did tell me they are in Orlando, Florida.
The name of the company he gave is "Senior Health Management." They are bathtub peddlers who target old people.
A search produced several companies with the same name, in different parts of Florida. At least one is listed as defunct. Calling numbers which should have been viable either produced a fast busy signal, or a telephone company message that the number is out of service.