If you said jumper to mean jump lead I would not understand you, and I would never use the word myself in the sense of someone about to commit suicide. But how you or I would use the term is not relevant at all.

The relevance is how a certain group of people in America (or part of America) at a certain time in the past used the word, and what they used it to mean. And from those lyrics in those songs where I have heard it, they are not singing depressing songs, and they are not singing about trains.

I believe that every time they are talking about some item of clothing, and I assume that it is not the same as what I would call a jumper.

Too bad that blues lyrics compendium has gone offline, so I can just quote some lyrics I remember. As already stated above, there are several songs with something along the lines of:

If you see my jumper hanging up on the line (or on the wall), then ....

I don't think they are singing about a railway line there, but a washing line, and the fact that it might equally be hanging on the wall ... anyway, it seems to be a signal for something or other, and not always the same thing.

More definitively from Tommy Johnson:

Would you wash my jumper
Starch my overalls
I'm gonna find my woman
She's in the world somewhere