Ms Jones said the charity bought the vehicle after a tidal surge destroyed much of the road at Spurn Point in 2013.
“We had to think very differently about how we could create access as you could no longer drive all of the way there,” she said.
She said the vehicle, which was used by the Army, had transported “thousands of people” across the sandy terrain but the cost of maintenance had “become too great”.
“We’re looking at exploring new and creative ways to transport people down to the point,” she said.
Ms Jones described the Unimog as “a real workhorse” and added it “certainly has life still within it” for a military enthusiast, attraction and other prospective buyers.
“The thing that really stands out for me is people’s joy when they see it and they’re really curious about the vehicle,” she added.
The reserve price for the Unimog is £12,000 and the deadline for bids is 12:00 GMT on Friday 14 November.