There's a good old word that doesn't get heard much these days: vamp. It means to accompany (a voice, a melody) with just chords, or a very simple dum-de-dum thumb-and-fingers type of thing. You can do it on any polyphonic instrument: when I was a little lad it either meant the piano or the mouth-organ; that was before guitars caught on. "Strum" would be the nearest string equivalent, although there's no reason why you shouldn't "vamp" a guitar; maybe vamping is a bit more adventurous than strumming!

There's "rapping" a banjo, of course. "Banging away" is something you can do on any instrument, although that's really a slang expression. "Strike up the band"?

A merry -- and a musical -- Christmas to you to, Wilfried.