OK, I might be getting in over my head but I'll try. Mine has a vacuum hose that connects to a tube coming out below the secondary diaphram, but I think this hose goes to the dashpot between the secondary diaphram housing and the choke. I think the dashpot has something to do with California controls.

On mine the dashpot is not connected to anything. Someone else may be able to help with this one. Also, I believe the source of vacuum for the secondary comes from a port through the secondary diaphram housing (no hose). On mine the butterfly was frozen shut but the diaphram was just fine.
I hope this helps. I'm not an expert and, like most people on this site, I've learned from getting my hands dirty and digging in. If I have given any misleading information it was not intended.
If you find that you believe your carb is not working properly they can seam a bit complicated but a kit costs about $20 and a rebuilt from Autozone is about $270. It doesn't take long to do the math. If you attempt the rebuild and your not to confident then take pictures of the linkage before starting and once you start taking the top cover off don't turn the carb over as there are check valve balls. Just follow the diagram that comes with the kit.
You may be able to find a working used Hitachi (which should be what you have) for a lot cheaper online or from someone on this site or you may consider changing to a Weber. I don't have any experience with them but people on this site rave about them.