Hi,
This is sort of a long post. I posted it here in case others need info about replacing the brakes or final drive oil seals.
I would read about the brakes in the 2 manuals you said above.
If your Cub is a 1952, with the original final drives, it would have the 1st style of brakes, with the rods made onto the brake bands.
The 2nd style of brakes are different, IH began using them in mid 1953.
Below is a post from the How To Forum on here about removing a Cub final drive, by Dale Finch.
It has lots of info and lots of pictures.
Be sure to put wooden wedges at the front axle pivot before removing rear wheels, or final drives.
A Cub is heavier on the left side, and they can tip over.
It is probably safer to take apart one side at a time, then one rear wheel and tire will be in place.
https://farmallcub.com/community/threads/left-final-removal-for-brake-lining-replacement.78436/
I would replace all the oil seals on the shafts the brake drums are on while it is apart. There are 2 seals on the left side, and 2 seals on the right side. Basically 1 seal inboard, and 1 seal outward of the brake drums.
TM Tractor Parts near the bottom of the Forums page has new oil seals.
Below is their listing for new seals, they are 2 different sizes.
This listing has pics on the page of where the seal goes.
The areas where the brakes are should be dry, no oil in them.
You can look in the holes in the casting where the brakes are with a light to see if the seals leak.
The final drives are held on by 6 bolts in a circle, they should be checked periodically to be sure they are tight.
The holes at the top and bottom of the mounting surface are for alignment dowels. Be sure they are there. If any are gone, TM Tractor Parts has new ones.
Below are pictures from TM Tractor Parts of the brake, and where the oil seal is.

I sent you a direct message.