I don't know if I would want to swipe my CC or bank card on an unknown card reader like this unless it was also set up for billing purposes for the use of the gym, this would have some very risky security issues which is not too uncommon to get a persons card info along with the pin if required to be entered, also like said if other customers showed up, how will you keep separate billing?
If it is just for access/lights then any of the door/gate access systems out there that is used for access will work, also another source is gated entry systems, I installed one for a storage unit place that if they don't pay their bill the operator can shut off the non-paying customers card to block access to the site, which was a networked card reader and the owner had a card writer on the main computer that he can write an access card on the fly when the customer rents the storage unit or shut off the card when they don't pay, just like motels use.
Here's a link to one such system I have used on many gated entry systems, but I would think it would be a little pricey for what you want to do
Select Entry Systems
If any CC/debt card will trigger it then way go to the expense of a fancy card reader since anyone with any type of card with a magnetic strip will allow the use of the lights, just use either a timer or motion detector system, or even a keyless alarm switch can be set up with codes to switch a 12 volt relay to turn on the lights, at least with a keyless switch you can have many codes that can be changed when a customer is no longer a member with this and a motion detector or programmable timer you can control access with the added function of the lights not just being left on?