You are correct. There is no reverse on that design of a 99.
Your machine used to have a rheostat in the base under the balance wheel operated by a steel shaft that entered through the hole in the right side of the base. Many were converted to conventional foot pedals.
That Case will not fit your 15 since it is shorter.
All that said, I love my 99s. I love the 3/4 size since they travel easier than my 66s.