Sounds like your car has air shocks, a common mod back in the day but not original equipment. if you look closely the lines should be either a whitish/clear or black plastic unless over sprayed with body color. As far as the radius rod/traction bar base 6 auto cars got none and base 6 std. cars received one on the right side. Only the sprint 6 4 bbl and v-8 cars equipped with a manual transmission received them on both sides. If you end up deciding you want one on the left side it is more complicated then just bolting one up even though the bracket is already on the diff. There is a support/stiffener plate that mounts to the floor pan that used to be impossible to find back in the day but I believe is being reproduced now. By the way if you did not find the Trans. fluid low after your test drive you may be surprised and find it works again after cooling down to help you with moving it around in the yard.