Foote did make gearboxes you can split but on the mustang they were sealed like I said before it only has 1 forward and 1 reverse gear I have owned ten of these machines over the years, they all had stiff gearboxes and every one of them freed up with a small amount of use, my opinion is you will be opening a can of worms for no gain by splitting it, why don’t you get the thing running and drive it first ?
Yep your right it is a Foote gearbox they were used on lots of cheap mowers in the 70s and 80s including some huffys and falls mowers My advice would be to warm the gearbox up a little and then keep moving it between gears, you will find it will loosen up