Here goes I hope this is correct but it is better than a guess.
The HAC device is a kind of booster valve. The weak force of the bellows is not enough to move a mechanical port switching valve reliably nor far enough because the movement of an atmospheric bellows is very slow. Manifold vacuum assists in moving a HAC valve. The bellows operates a valve that allows manifold vacuum to operate a port switching valve by means of a diaphram. So there are two valves in the HAC device. The switching port allows atmospheric air to enter the carbs air jets at high altitude only. There are 3 air jets in the carb which are used to lean the fuel mixture.
The HAC device switch port needs to be in parallel with the EBCV switch port because the HAC's switch port is closed under normal low altitude conditions. I found another vac hose sticker from Need info (sticker under the hood) of 1988 Toyota Corolla FX
Where I found this pic
This vac hose sticker shows the EBCV and HAC as two separate devices. Notice that two of the EBCV and HAC switch ports are in parallel as can be seen from the vac tees connecting the two devices. This sticker is way easier to follow despite the wrinkles and gives some important clues. Testing indicates that the "S" connector on the EBCV feeds air into the idle jet and the "M" connector feeds air into the primary jet. These two jets are also fed by the HAC. The HAC feeds the secondary jet thru it's own port which is the only port not controlled the by the EBCV.
Notice that manifold vacuum is used only by the HAC not the EBCV, which proves that manifold vacuum is not applied to the carb jets. The HAC and EBCV switch ports allow atmospheric air to enter the carb's air bleed jets due to a small vacuum that originates from the jets.
Refer to the hand drawn vac hose diagram at the top of this thread. In the pic it says EBCV (14) there are 3 connectors in a row and one connector below. I forgot to mark the connectors, so lets say that from left to right the top row will be "a", "b", "c" and the lower will be "d". The "d" connector goes to manifold vac through a check valve (18)
The hose from connector "a" of the EBCV goes to the primary fuel jet and the hose from connector "b" goes to the secondary fuel jet. When the car is idling, removing connector "c" will stall the motor because the idle circuit draws air - not fuel. If you put your thumb over the open hose the vac can not be felt as it is very minute. Here is what happens if you try to drive an 88 corolla (same EBCV as the 89) with the vac hose from the "a" connector removed
From this link Issues after installing new carb
First problem is during acceleration. Under 3k rpm the car accelerates very unevenly and sometimes not at all. It seems to run best in that rpm range when I only give it the smallest gas possible, anymore than that and it doesn't work. I feel like it may be too rich... When I give it gas and quickly back off the accelerator it seems to recover. After 3k rpm the car runs like normal and if i dump fuel long enough the car will switch gears and accelerate hard.
The above poster thought that the car was accelerating poorly due to a rich condition when in fact it was due to a lean condition.
Testing revealed that plugging off the PCV valve made a huge difference in O2 sensor output volts at idle. With the PCV as is I measured a steady .050 volts at idle - thats right 50 millivolts. When I plugged off the PCV valve, the volts jumped up to a steady .6 volts or so. The variability of the PVC makes accurate testing of the O2 sensor impossible unless plugged off. At least the O2 sensor works well - the slightest hint of oxygen smashes the volts down real quick.
I tried to see if I could get the car to run at less than .050 volts at idle. I removed the hose going to connector "C" of the EBCV and quickly put my thumb over the hose so the car would not stall. I very carefully released my thumb pressure from the hose and sure enough the o2 sensor volts started dropping. When it hit about .025 volts the engine stalled. Strange thing is the EBCV is supposed to work even at idle but I could not get a response from it. (Found out what was wrong later in this thread) Many car web sites report this same thing about the EBCV that it does not work. I wonder what goes wrong with it.
I tested the EBCV itself by putting batt voltage thru a small test light to the EBCV electrical connector > there was a click noise and the engine stalled so I know the EBCV idle switch port is working but the ECU simply is not sending it anything. I found out later that even though this test worked, the EBCV idle switch port would not actuate with the signal that the ECU was sending it.