Melt the white chocolate and coconut oil together in a microwave-safe bowl in 30-second bursts, stirring between each until completely smooth.
Lay two sheets of parchment side by side on a flat surface.
Hold a pretzel rod over the bowl and spoon white chocolate over three-quarters of its length, turning as you go to coat it thinly all around.
Lay the rod on parchment and use a fork or spoon to drizzle additional white chocolate over it in quick back-and-forth motions to create layered bandage lines.
While the chocolate is still wet, press two mini candy eyeballs onto the uncoated end of the rod.
Repeat with remaining rods, working quickly so the chocolate stays fluid.
Leave the rods flat to set for 20 to 25 minutes. Once firm, stand them upright in a tall jar for display.