Appreciate you accepting this as the answer to your question.
My research indicates that the National Labor Management Panel was
reactivated by President John F. Kennedy in 1963. He made appointments
to that panel, and President Johnson made some appointments after the
death of President Kennedy.
Here is a very brief mention of the Kennedy reactivation of the panel,
from the "JFK Link" web site.
"... Statement by the President Upon Reactivating the National Labor-
Management Panel. May 26, 1963"
Here are a few appointees from the period starting in 1963.
Marvin J. Miller, of baseball fame.
Early Career and United Steelworkers of America.
National Labor-Management Panel 1963-1966
Here is one of the Johnson appointees.
"June 4, 1965. Letters Patent appointing J. Curtis Counts as '...a
Member of the National Labor Management Panel.' Countersigned by
Dean Rusk as Secretary of State, with a large white wafer seal.
Signed by the President in grey ink below the printed text, 'Lyndon
Those appointments, for the period starting in 1963, and from further
research, ending in 1966, appear to be the last appointments that were
made to the panel.
In other words, there does not appear to be anyone currently appointed
to the panel at this time.
If you need any clarification, please feel free to ask.
Google search on: "Labor Management" Panel
Google search on: "National Labor Management Panel" 1963..2005
Looking Forward, denco-ga - Google Answers Researcher