The fireman in the 1916 Ford might be a young Walter Beatty who was the curator of the museum for many years when it was on Duane St.A picture taken at the 1939 Worlds' Fair: the 1939 Mercury of the 36 Bn along with the department's 1916 Ford . . . which is still on the roster at the museum. Sharp eyes will note the FWD behind them.
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Here's a more recent pic of the Ford:
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Both pictures courtesy the FDNY Museum.