Ah yes. And the Republican President of the time was well known for saying, "Mr. Gorbachev... BUILD UP THIS WALL!!"
You haven't picked exactly the best examples. In the USA, over 60% of our illegal immigrants are due to overstayed visas. The Wall does nothing for them. Another point: the #1 illegal immigrant in the USA is Canadians: a Mexian wall is on the wrong part of the country if you're most concerned about undocumented people.
The thing we need, and something I'd support, is proper enforcement of our laws. Like employers who hire undocumented workers should be better punished.