I made repairs on a golf cart that the original owners cousin authorized and now the owner is trying to get it back without paying for the repairs cost
Thanks for this question, however, this website is for construction law matters and does not deal with motor vehicle questions. The use of the words "mechanics lien" is the former terminology for what is now known as a "construction lien" allowing contractors to assert a lien against the real property for work completed on the premises.
While Florida law generally does have a number of statutory provisions for liens to be imposed on motor vehicles or vessels, you will have to look elsewhere for this information.
Best of luck for the new year.
Internet research regarding liens AND vehicle repairs or you could try posting on more generalized attorney question and answers sites such as AVVO, Justia, etc.