Slick 60's

Okay, Can I assume that by putting the drill in the reverse direction that the gear inside the trans must be a left hand gear?

What transmission are you messing with? I have the gear out of a 3 speed toploader. I also have the driven gears with various teeth counts. They only work on the one that has the cable go in above the gear. The ones that have the cable go in below the drive gear are pitched backwards.

I had this same thing happen when I stuck a drive gear out of the transmission from a 80 model in my transmission. the driven gear/ cable go in under the gear so they were backwards.

As everyone is saying---you have a mis-match with the gears.

Running the drill in reverse is correct, that is the way the cable should spin.
You just need to get the correct matching gears. The cable will still turn the "reverse" direction.