Modern Vespa

I've been wanting to ak this for awile now but it always looked stupid once I finished typing it.

Anyway, what is the purpose of the second small lamp in the headlight housing?

It is always lit when the main lamp is lit.

It is the city light: city light on S 150.

I've a two position switch; always on, low beam or high beam.

That second bulb mounted off center in the housing is aways lit, no matter the position of the switch.

Same as me. I suspect (but have not had this confirmed) that Piaggio uses the same headlight assembly for all the LXs, but use different switches. Those being exported to countries where an always-on headlight is mandatory (like, N.America) get one kind of switch. Otherwise, they use a switch that can turn on and off the headlight, and leaves on the parking/city light.

I only am guessing at this given the post I linked above, and an older European car that had a similar odd set up (you turned on either the left only, or right only, parking lights when headlights off. Turn on headlights, and both sets of parking lights went on).

That's the day running light for the rest of the world. Here in the states, it is mandated that our headlights be on all the time. In other markets, they can turn their headlights off, and that is a daytime running light.