Chase effect single line vs polyline?

Is it possible to have a chase effect run around a collection of single lines that form a shape?
As far as I can tell, as a group of single lines the chase just runs left>right over the whole group at once.

If I build the shape out of a polyline, the chase rounds around all the way it pixel-by-pixel as expected.
But by drawing a polyline, I can't break that line down into smaller lengths (like separating verticals and horizontals) for other effects.

Does that make sense? Am I correct?

How can I get a chase to run all the way around the shape of a group of single lines?

So I think there's a couple of things here.
1) is that you can create a submodel - to split a poly line down into smaller lengths for other effects
2) is that I think you're using 3D -- I suspect you can do some of what you are after by playing with some of the views within (eg: change the view to directly above the roof instead of the front)

Onthe group method- if you use that method, and want to chase from A to B to C to D across your segments - the render style for the group set as "Single Line" - this will bump the strings up next to each other, rather than "stacking" them - which would cause A-D all chase simultaneously.

Thanks I'll look into both of these as I think the submodes + render style will likely solve what I'm after.

Unfortunately I didn't get to the 3D model this year tho that would have been ideal... next year!