It's interesting that so many really over the top sentimental songs, poems, short stories, etc. came out of Victorian times...the sort I cluster under the "Songs I Learned at My Mother's Knee (and other low places)" umbrella. Songs about violet sellers, drunken fathers, dead mothers are a way of safely evoking emotion in a changing world where change is scary and authentic tragedy is overwhelming.
My own sentimental BS litmus test is definitely manipulation. Sentimentality may ellicit tears, especially if it's been a bad day, a bad night, whatever, but it is a cheap shot, calculated to wring out emotion at all cost, authentic or not, and I resent this calculated manipulation. (I find movies like E.T. in this category as well.)
In much of traditional music/song, there is authentic distillation of emotion, both at inception and thru the folk process, that rings true. Yet its accessibility allows us in the 21st century, to, if approached with the proper respect and care, let this music speak directly to us and even through us. The connection for me is as real, and thrilling, as putting my foot into a stone stair hollowed out by hundreds of years of wear.
And it is usually true, for me, at least, that the songs that truly move me are very spare traditional songs, traditional in nature if not in fact, where little is said, much implied. Pain and tragedy is explained and accepted, wth no need to ask or beg for anything from the listener.
Sentimentality is all about getting the listener to respond. It's a power play.