Most American(or “Americanized) instruments had at least 4 strings from what I know(I’m a drummer so this is going to be a best guess)...and it looks like that plate had 4 tuners in-line(part of plate broken with one missing tuner)...so...it COULD be a mandolin. But you know...I really can’t say for sure.
One on each side would make it a six string - as in guitar. I think the break was at the post that goes through the head. Could have been three string tuners in the strip.