I moved my mushroom up a little and when I lifted it out of the sand I saw this long tube-like thing. The second photo shows a translucent feathery thing I noticed last week and I'm guessing this is what comes out of the end of the tube from the first photo.
Phew! Thank you, Diana. I just Googled them and I'm reading they prefer a sandy location. I just pulled the rock it's attached to out of the sand because I wanted to raise my mushroom a bit, but I guess I should move it back to the sand. The mushroom and feather duster are attached to the same rock.