I don't know anything about BS34s, but the BS38 enrichners and plungers I think are similar. On those, there's 3 passages:
1. Air into enrichner body from vent under the diaphragm.
2. Fuel/mix into enrichner body from carb/bowl.
3. Air/fuel mix out of enrichner body to large port in throttle bore.
When the plunger is down, it simultaneously plugs the bottom fuel/mix port, and its cylindrical body blocks the connection between the air-in and air/fuel mix out. The "choke" is off.
When the plunger is up, all 3 passages are connected. The "choke" is on.
Enrichner fuel enters a small hole at the bottom of the float bowl, is metered by a tiny pressed-in brass jet, and fills the starter well.
(Thanx to 5twins for these bowl pics)
An intermix/emulsifier tube, coming down from the upper carb body, resides in this starter well, where this bowl fuel is mixed with a separate bleed air source (top of bowl chamber).
The emulsifier (percolator, aerator) tube serves to intermix bleed air with raw fuel to produce an emulsified, foamy fuel. This is then delivered to the bottom port in the enrichner's plunger body.
This is similar to the jets, air bleeds, and emusion holes, in the other jetting systems. So, the choke/enrichner system is like its own little independant mini carburetor, running in parallel with the main carburetor.
So, this choke isn't really a "choke" in the traditional sense (like on carbs with a blocking butterfly plate). It's really another carburetor, setup to be WOT and rich...