Tony wrote:

look easiest way to solve mystery is hook up one light bulb
and measure the current on both wires and you will find
that both weirs have same current flow, that's easy enough,

In a 3-wire circuit you have two hots and a neutral. If you put a light
bulb between each of the hots and the neutral, there will be no current
flow in the neutral.

In essence, the current flows up one hot, through the bulb, through the
other bulb, and back down the other hot. (It's like one hot is
positive, the other is negative, and the neutral is zero.)

The neutral is only needed for the case where the load on each of the
hot legs is not equal.

Chris