He received fatal injuries when he was trapped by the machinery being used for the project.
The Health and Safety Executive’s Mines Inspectorate is investigating the accident, with the full co-operation of the museum staff.
Mr Buckingham, from the Grimethorpe area, was part of a team of contractors and was not employed by the museum.
A spokesperson said: “We are very saddened by this incident, and extend our deepest sympathy to his family, friends and work colleagues.”
The incident happened before the museum, pictured, was open to the public, and officials said there was no danger to visitors.
Although no longer a working coal mine, the tourist attraction still operates under the stringent regulations of the Mines and Quarries Health and Safety legislation, regulated by HM Inspectorate of Mining.
The museum re-opened on Thursday. Underground tours have been temporarily suspended but are expected to resume next week.