Some Brexiteers suggested that Brexit would be a softer affair, in the lead up to the referendum.
Tory peer Daniel Hannan (formerly an MEP) said in 2015: "absolutely nobody is talking about threatening our place in the single market". And yet we did leave the single market, as part of the hard Brexit pursued by the Tories.
But yes I suppose other leading Brexiteers didn't make details explicit. Perhaps, after the Brexit referendum, we should have had a second referendum to determine what shape Brexit should take. We could have remained in the single market for many industries (similar to Norway/Switzerland/Iceland) or the customs union (similar to Turkey), or both.
Brexiteers are famously supportive of "democracy" so they shouldn't have had any objections to a second referendum.