After speaking with Ana Galindo-Marrone, Chief of the Hatch Act Unit of the Office of Special Counsel and doing some more research, I've come to understand that the while the Hatch Act states that federal employees are disallowed from making a "run for the nomination or as a candidate for election to a partisan political office," the prohibition does not disqualify a federal employee from running for office. Rather, it visits consequences on the employee if he or she does run. For a good discussion on this issue, see Judge Joseph E. Irenas' opinion in Merle v. United States, 217 F. Supp. 2d 560 (D.N.J. 2002).
Stated another way, if a federal employee were, for example, to run for county freeholder, neither state nor federal officials could declare the employee disqualified from running, or even from serving in office if he or she was elected. Rather, the federal Office of Special Counsel could bring charges (up to and including terminating) against the employee for violating the Hatch Act's prohibition. Those charges would be adjudicated before the Merit Systems Protection Board.
Against this backdrop, it would appear that David Gonzalez was not "ineligible to run for office," as I stated in my original blog article. Rather, he appears to have been "eligible" to run and, after having won the primary, his decision to withdraw and the Fairfield Democratic Executive Committee's (FDEC) decision to replace him with Bernard Manson may have been appropriate.
There is still a question regarding whether Gonzalez withdrew from office promptly enough to avoid disciplinary action by the Office of Special Counsel. And, I haven't researched whether the FDEC handled the replacement of Gonzalez with Manson in a manner consistent with N.J.S.A. 19:13-20.