The attribution, by the Babylonian Talmud, of this Targum to Jonathan ben Uzziel is suspect on several counts: among others, the silence concerning Jonathan in the parallel passage in the Palestinian Talmud, and the fanciful suggestion that Onkelos=Aquila and Jonathan=Theodotion. The attribution, therefore, is not to be taken as historical fact. The Talmud may have been attempting to enhance the authority of the Targum by claiming authorship by a disciple of Hillel, which Jonathan was.
It is generally agreed that the author of the Targum Jonathan is unknown; in fact, it is preferable to consider multiple authorship. For while language and translation techniques are uniform, there is variety from book to book.
Buy Targum Jonathan of the Form Hc by Daniel J. Harrington, SJ from Australia's Online Independent Bookstore, BooksDirect.