@cicerone imposter,
You are right - the Brits did not give Gibraltar much thought.
Nor were they well informed about the consequences of an exit.
Politicians have for years ignored the common person´s feelings regarding EU and that not only in UK.
There is certain more or less aggresive parties and people against EU, some going as far as calling it EUDSSR. They want out.
On the other hand we have the almost uncritical EU people who think that EU will lead to heaven on earth.
In between is the great majority, which is critical to EU, but as a rule want to stay and do not want an exit.
Before Brexit there was a certain mistrust in EU in Sweden and Denmark, which right after Brexit changed to greater trust in EU.
8th of June 2016 42% of the Danes wanted an election regarding EU
4th of July 2016 32% wanted Denmark out of EU.
In May 2016 49% of the Swedes found EU ok and 23% were against EU.
In November 2015 the OK went down 20% from 59% to 39% and the ones being more negative went up 11% to 52%
All of this can tip very easy in any direction