As an excellent example of #2 we've got Bir Tawil and the Halaib Triangle - both exist along the Sudanese-Egyptian border. Two different historical border drawings have been presented which each argue that the Halaib Triangle belongs to a different country and the triangle has 27k inhabitants. Funnily enough, each map that yields that valuable chunk of land to each country actually yields that Bir Tawil should be possessed by the other country (and Bir Tawil is comparatively worthless). As a result neither country claims Bir Tawil since it could be seen as an admission that the other country has a rightful claim to Halaib Triangle.

Usually these weird chunks of land that lay unclaimed are usually the result of agreements or contests around more valuable chunks of land that cause voids in the border - sometimes just due to historical oversight.