undesired oscillations

hello, I have another question, which perhaps I already asked years ago, for which I did not obtain answers that I could verify or that would help me satisfy my curiosity. I should preface that the instruments I tune are almost never high-end and/or new. It often happens to me, from the cantabile upwards, that a string of the choir, left free on its own, produces a vibration very similar to a beat, which slows me down in searching for the unison, which then is not cleaned up due to this interference. I have tried everything that has been suggested to me without obtaining the much-desired clarity. I changed the string, plucked it to exclude the responsibility of the hammer, tried tensioning it much more and much less to exclude the disturbance caused by an incorrect proportion between the length of the string and the frequency assigned to it. I also tried to dampen the strings without dampers with no tangible result. I am adding a detail that might suggest science fiction: almost always, 90% of the time, it is the string to the left of the choir, the most mischievous one. thanks anyway