Airlines don't provide the wheelchair service, third party companies the airport contracts with do. You can request a wheelchair when you check-in and you can also request it in your reservation to help ensure one is available for you. Any specific policies related to the wheelchair service would need to be answered by the airport or their service provider.
Here is info about requesting wheelchair assistance:
https://www.southwest.com/html/customer-service/unique-travel-needs/customers-with-disabilities-pol....
When booking a new reservation, Customers may use the “Special Assistance” link on the Passenger & Payment Info page to indicate that he/she requires assistance. When booking online, Customers may notice that there is a link (identified with an italicized "i") that directs the user to the details of our policies for assisting Passengers with disabilities. After the Customer has selected his/her option(s), the Customer should scroll down and complete the booking process.
If a reservation has already been created, simply click on the “FLIGHT | HOTEL | CAR | VACATIONS” link located on the top of our home page. Then, select “Manage Reservations” from the “Flight” column, input the required information, and select “Search.” From that page, click on the "Special Assistance" link under the Passenger name. Once a Customer has added his/her option(s), the Customer should click “Update Information” and the information will be saved to the Customer’s reservation.
Customers may also advise us of any disability-related travel needs at the time of booking by telephone or, if a reservation has already been made, by calling 1-800-I-FLY-SWA (1-800-435-9792) prior to travel.
--TheMiddleSeat
