Hi!  I have been scouring the internet and haven't been able to find my answer. Does anyone know how to make those thin horizontal lines on this cake pictured below? I have made the "rustic" horizontal lines with a pallet knife but that is much wider then these. Any insight would be greatly appreciated!

I've never made the small lines like those pictured, but I would think you would make them the same as the rustic finish done with a small spatula, but using something smaller like the end of a spoon handle.

Use a (new!/sterilized) wide tooth comb.  Or pipe the lines w/a 2 or 3 tip.

Here is a tutorial showing how to do those lines.

The picture is kind of low resolution, so I'm just wondering if that's actually a design done with a petal/rose tip, rather than the pallet knife technique. It looks too ruffly and narrow to me for it to be the dragging of the pallet knife through the frosting. Just throwing that idea out there. Could be someone going full circle around the cake with a petal tip. Looks like the ones I've seen my coworkers do.