There is a certain piano element I hear in certain classic country songs, where the piano seems to play backup to the vocals for the extent of one verse. It has a feel that the person is sitting there "tickling" the keys.
Three songs that have this element would be
1) Randy Travis On the Other Hand between 1:30 and 2:10
2) Conway Twitty and Loretta Lynn After the Fire is Gone between 1:35 and 2:10
3) George Jones These Days (I Barely Get By) between 0:00 and 0:50
If anyone can identify this piano style, I would be thankful.