2002 Ford Mustang Fluid leaking from center rear of vehicle

My very first leak on this vehicle. I am finding slight puddling of a medium consistency fluid from the center of the rear axle area. Transmission shifts and operates normally. No indication of noise or stress but definite leak in that area.

Receiving advise of new transmission or seals. Would appreciate any recommendations of what to check to ensure I am not going to be replacing a perfectly good transmission. This vehicle has been serviced regularly as directed by the manual until I am being declined on changing the transmission fluid now that the car has over 100K miles. Never any issue with poor shifting or issues with transmission.