The City of Wilmer does not issue or require a "business license."
You will need a certificate of occupancy for your place of business (contact the city's Building Inspections Division, 128 N Dallas Ave., 972-441-6373). If you are working out of your home, you may also need to obtain a certificate of occupancy.
For food establishments, a health permit is required.
For alcohol sales, an alcohol permit is required.