Is it Islamically permissible to use a mouthwash that contains alcohol?

The alcohol that Allah prohibited is the Khamr ( intoxicant alcohol ), and not every alcohol is an intoxicant alcohol.
The intoxicant alcohol that we find in foods and beverages nowadays is ethyl alcohol.
Mouthwash products usually contain menthol, thymol, and eucalyptol alcohol which are not intoxicant alcohols. Therefore using mouthwash products that contain alcohol are permissible for medicinal use only. If it is not for medicinal use, then using mouthwash with alcohol ingredients should be avoided because of the existence of a permissible alternative which is alcohol-free.