With 1/8th, I have done it by tapering and adding a small piece of tape and just milking it through. Open up strands where you want to start the bury, Feed the pointy taped end in and start milking. It takes some patience at the start but after the first inch or so you can walk it through pretty easy. As a disclaimer the smaller the rope the need to have the "tools" of the trade become more important. 1/8 is the smallest that I have been able to, or willing to use the tape method, anything smaller and I have to use a wire out of an old telephone cord.
“Never argue with stupid people, they will drag you down to their level and then beat you with experience.”
― Mark Twain