There are many ways to clean ceramic rods or stones.
I use a pencil eraser, too. That should do the job quite well and remove most of the metal. From time to time I use a powdered scouring agent, too. I think it is Ata (BKF is expensive in my country). A nylon hand brush is what I use. A Scotch Brite Pad will work, too. Or a toothbrush.
You could even use toothpaste. Dish detergent might also work (works good with Fällkniven's ceramic). With Spyderco or Lansky I prefer the pencil eraser + scouring agent.
I haven't tried the following ones: Lansky or A.G. Russell Eraser Block. Mr Clean Magic Eraser.