I've never heard of a trip-line running back to the boat or attached to the anchor rode in any way. That sounds like danger waiting to happen.
My trip line is longer than the water is deep at high tide so it won't pull on the anchor at all. I run the line up to the float and through a shackle and then put a little weight on the end of the line. The weight pulls the slack out of the trip-line and keeps it floating plumb at all stages of tide.
Remember to attach the trip-line to the other end of the anchor so if you need to use it you are pulling the anchor out backwards (which is how you get it unstuck).
who is staring at the sea is already sailing a little