Mixup My parts book shows two numbers
B7C-8112108-A was for fordomatic 3speed L/D and 3 speed M/D
B7C-8112108-B was for 3speed H/D and 4speed L/D And four wheel drive
So looking at your data plate will determine which cover your truck came with.
I'm assuming the _B is the low profile. Its what I have in my 59 4x4. I've never noticed a high profile cover, but sometime I just don't pay full attention.