Hi Herbert,
I read your original post and I'm not sure if I can accurately answer your question. The light sets I'm familiar with from my childhood had the transformer permanently in-line with the low voltage side coming out of the transformer. The transformer itself was a sealed unit about the size of a pack of cigarettes. If your strings have a spade connector on the end, they might be of U.S. origin. The real question is whether the bulbs are of the C6 or C7 type. If they are C7, that would account for the parallel wiring and the spade connector at the end.
Regards,
Scott