Thanks for your help and suggestions. Three weeks ago, I found my 1978 Carlisle in the basement and plugged it in for the first time in 20 years. It worked, but the wax would mostly just remain in a throbbing vertical column formation, as shown in my profile photo. Rarely would it ever do anything else. Also, the liquid would become quite cloudy after running the lamp for a few hours.
After two weeks of operating the lamp a few hours daily, it improved slightly. I topped off the liquid with distilled water, and added SLES a bit at a time until I got the desired motion from the wax. What a difference!
The liquid cleared up completely, and now the lamp performs as well as it used to when I was a child. There is a lot of motion in the wax now, and it forms a wide variety of different formations and sizes of globs of wax. I was delighted to be able to so easily restore proper operation of my old lamp.