Don Richardson has been a member of The Wagonmasters, The Reinsmen and The Lobo Rangers. According to Dave Bourne, he is one of the best rhythm guitarists in the western field. He also plays stand-up bass, 4-string banjo and can sing all the harmony parts of all the songs. The Sons of the Pioneers' harmony was unique and we asked him to describe it for us.
For the most part, the Pioneers used 3-part harmony structured in this way: The lead singer sang the melody with the tenor above the melody and the baritone below. This is what I refer to as "basic" 3-part harmony. As the melody moves, the tenor and baritone move in parallel - hence "parallel harmony". The exceptions to this are several, and I think this is where you experienced them "trading places".
One example of this would be if the baritone was singing the melody on a particular song, the lead singer would sing a harmony part above the melody and the tenor would sing a harmony part above the lead singer's part. I call this "stacking the harmony on top". Conversely, if the tenor was singing the melody, then both the lead and the baritone would sing harmony parts below the melody, which I call "stacking the harmony on the bottom". (Again, other people may use different terminology)
Other exceptions to the "basic" structure is a combination of the "basic" and the above two examples. For instance, a song might start in the "basic" mode but as the song progresses the melody might go so low that the baritone has difficulty staying below the melody, so at that point the baritone would switch his harmony above the melody and the tenor would move above the baritone. In this case the baritone is actually singing the tenor part and the tenor is singing the baritone part an octave higher. I believe this is what Bob Nolan was saying in his quote: " . . . the tenor would be the high baritone and I would come up into the low tenor." The inverse would be if the melody went too high, then the tenor would drop below the melody and the baritone would stay below the tenor. These last two examples are essentially the same as the two "stacking" examples, the difference being that in the "stacking" examples the melody was sung by either the baritone or the tenor, whereas in the latter two examples the lead singer always sang the melody while the other harmony parts had to adjust around the lead singer. (This is the way the Ames Brothers and the Andrew Sisters structured their harmony. Ed Ames and Patty Andrews always sang the melody in their respective trios, while the other members always sang harmony around them.)
Another method of harmonizing that can be used - primarily when a melody has such extreme range that it is difficult for any singer in the group to reach all the notes - is for the melody to switch from one singer to another as it goes higher or lower out of the lead singer's comfortable range. In this case, the tenor or baritone picks up the melody when it reaches the lead singer's cut-off point. The lead linger is then singing harmony. The process reverses itself when the melody comes back into the lead singer's range.
Any and all of these methods can be done easily and smoothly if done properly. This is why it is difficult for the listener to know what's happening. As you said, it is often hard to find the melody. Unfortunately, the only way to know for sure is to actually know what the melody is. I believe the Pioneers used most of these methods at one time or another, depending on the song and the personnel in the group at the time. My guess is that they didn't have to use the last method much, if at all, because they all had such good vocal range.
Occasionally the Pioneers used 4-part harmony. The 4th part was a bass part, usually sung by Hugh Farr, and was usually independent of the other 3 parts. Sometimes it was a simple bass line consisting of the root note of the chord. Other times it might be a moving line that fit within the chord but was not necessarily the root note, or it might be a counterpoint to the trio, adding another dimension or syncopation to the song. An example would be "Too High, Too Wide, Too Low".