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Sorry Mike, but the F-SD uses a transmission-mounted parking brake drum, not like the axle mounted brakes on the F-250 and F-350. It does have its own lubricating fluid that is separate from the transmission, but it uses transmission fluid to lubricate itself.
From the workshop manual:Fill the parking brake to the bottom of the filler hole with Motorcraft MERCON® Multi-Purpose Automatic Transmission Fluid, XT-2-QDX or DDX or MERCON® equivalent.
If you need more information go Here that takes you to section 06-05 of the manual. Then navigate yourself to the section labeled "Disassembly and Assembly - Brake, Parking, Transmission- Mounted. The fluid spec above comes from step 42 of the "Assembly" process.