Here's a good tutorial on how to care for caned furniture: https://www.wickerwoman.com/articles/cane-furniture-care
Clean grimy or dirty cane seats with a wood soap such as Murphy's Oil Soap or mild detergent in warm water, using a soft cloth or perhaps a soft bristle brush.let dry thoroughly before sitting on the caning so it doesn't get stretched out. to keep it from getting brittle-- lemon oil, orange oil and mineral oil. Occasionally tung oil, varnish or even furniture wax are used as a finish on the cane without harmful effects.removing extra and drying thoroughly.
Wash gently with a soft scrub brush with Murphy's Oil Soap. Dry quickly.