On the GY6 there is only one vacuum line on the carb that should be hooked up. It may be the one you are talking about. it's on the right side (opposite of the FEV) and it connect's directly to the intake manifold to that little barb. Sometimes there may be a T coming off a tube from the intake manifold but you can remove it and run a line strait from that vacuum hose. The T I think, was meant for a gas tank with the pump on it.
It takes a lot of muscle to pull the cable into reverse without the lever. Even if you get it pulled out its hard to get it to stay there. The good thing about this is, is if your on a trail and the cable breaks, it will break in the forward position.
This looks to be like the reverse lever you'r talking about from ebay. The one that came with my gearbox sucks! It is the type you have to push forward to go into reverse, and when I'm buckled in my seat belt it can be hard to get it all the way there. I will be switching to one of these real soon.
http://www.ebay.com/itm/Reverse-Leve...ht_2518wt_1163