This is a great example of how hard-to-use GIMP is. The stuff is right there in front of you, but it is mystically difficult to actually use. Even after seeing the other answers, I still could not make it work, but persistence paid off. Perhaps this will help:
If a selection is active, optionally use Select | None to start a fresh selection.
Raise the Layers, Channels, Paths, Undo - Brushes, Patterns, Gradients dock if it is not already raised. When not raised, it is listed in Windows | Recently Closed Docks.
Click the Layers tab on the dock, click-select the layer to draw on, and make sure it is visible.
Click the Paths tab on the dock, click-select the path to trace, and make sure it is visible.
On the dock, right-click the path to trace, and choose Path to Selection.
There are several ways to select the path, add a path to the selection, etc., but this is possibly the simplest for sake of teaching. In any event, a selection should appear that is tightly fit to the path. This default selection is almost certain to require modification...
Using the menu, expand the selection with Select | Grow. A dialog will raise. On it, grow the selection by at least the radius of the of the line to be drawn and click OK. Growing the selection larger is generally not a concern with respect to stroking a path.
Confirm that the marching ants bound an area sufficient for the stroke to draw, and that the area is within current selected layer boundaries. As needed, make adjustments to be sure the stroke can be drawn in the selected area.
On the Paths - Brushes dock, right-click the path to trace, and choose Stroke Path.... A Stroke Path dialog is raised.
Configure the Stroke details and click the Stroke button.
The desired results appear consistently, though mystically, the stroke jaggies can be quite terrible (at least for the path newbie). Anti-aliasing was my friend.
Use the rectangle selection box, and under the Edit menu, hit Stroke Selection. Select your options from there, and hit "Stroke" to apply the stroke.