Executive search firms need a good resume from you, but they also must have a search assignment that matches your background before they can be of service. Headhunters do not market you. They find the best candidates for client job openings. Their clients are companies that pay their fee or retainer. Don't expect a headhunter to make you her number one marketing project. Conducting your search campaign isn't her job, it's yours.

No one can help you in holding a good job except Old Man You.
Edgar Watson Howe

It is easier to do a job right than to explain why you didn't
Martin Van Buren