That "wire" is the overflow, as mentioned, it's actually a just a drain tube. If the engine running changes, if that is plugged vs. unplugged it tells me you have other passages in the carb that are probably plugged (the jets). Although, with the drain closed, plugged vs. unplugged shouldn't make a difference.
I am guessing if you just take it apart (carefully), clean everything (carefully) and put it back together (carefully) you may get it back to operating correctly.
The jets are very tiny holes in brass screw pieces in side the carb that get plugged with solidified fuel (especially if left sitting with modern fuels). Older fuel used to leave "varnish" deposits, modern stuff leaves a white snot shit that is just as if not nastier than the old varnish. You need to be careful with carbs as any ham-fisted repair attempts will fail with only expensive replacement parts as the cure.
You are on the right track wanting a carb "blueprint", you need to search for the carb's manual (which will probably end up being an exploded diagram).
If the picture you posted is really your carb, it's pretty simple. The biggest problem with these will be the soft brass screws getting damaged during removal. You need to have some decent screwdrivers to get them out in some cases.
1974 Suzuki TC-185 (The little 10 speed)
1986 BMW K75c
Yes! Whenever bicycles are broken, or menaced by International Communism, Bicycle Repair Man is ready!