Hello,
Having disassembled a few Singer 27/127s, I can tell you that is definitely not a part that belongs to the machine itself. The clip thingy is absolutely a piece of a tucker attachment, but the zig-zag bends were put into it by someone, as it is normally quite straight on both sides. Honestly, it looks to me like the whole was put together by someone (or someone's husband?) as a helping device to be fastened to a table or surface with the clamp end, and then to hold something that could be fitted into the clip end. The clip doesn't look strong enough to hold say, a manual or book pages, but might hold pieces of fabric or some such.
Matt