This can be a pain in the ass! And take some of the fun out of character sculpting. The best solution that I have I’ll illustrate here.
I've sculpted the head details, spotted in the ears and marked the eyes with two small beads. Now he needs a neck. On the final toy the neck will be flexible.
Using thread and Cyanoacrylate glue (Crazy Glue) wrap the wire with a nicely spaced coil of thread, secured with glue. Use some brand of "Insta-set" or "Zip Kicker" to instantly dry the glue.
Microwave the clay so it’s hot and liquefied in the center, spread the liquefied clay on the threaded wire. Once it cools a bit there’s a solid base to sculpt up. With Super Sculpey it’s a similar technique, except I smear the clay into the wire to get that sticky base.