President Trump's presidential proclamation specifically defines the countries affected by the ban as the 26 signatories to the Schengen Treaty:
For purposes of this proclamation, the Schengen Area comprises 26 European states: Austria, Belgium, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, and Switzerland.
However, four European states also maintain open or semi-open borders with the Schengen area, namely Andorra, Monaco, San Marino, & Vatican City. Clearly travellers from these countries will also be subject to the separate ban on people that have visited Schengen countries in the last 14 days, but considering the (semi)open borders, there should be no way to definitively prove this status one way or the other.
Are these countries exempt from the ban? Is this an oversight by the Trump administration, or do methods exist to identify travellers from these countries who have recently returned from the Schengen area proper?