The Polska efter Johan Ersson och Johan Olsson we have through a fiddler named Carl Persson in the province of Södermanland. Persson, born in 1864, was the son of another fiddler, born in 1838.
Carlsson learned the tune from two friends of his father, the above-named Ersson and Olsson.
Carl Persson played 10 tunes in 1930 for inclusion in the Södermanland volume of Svesnska Låtar. This is number 145 in that collection.
Here is a video of me playing the Polska efter Johan Ersson och Johan Olsson.