Curious - Three Vacuum Lines Coming Out of a Round Device, Device Name/Function?

This is on a 1990 Ford Escort GT. Vacuum input comes from a T fitting in-line with the EGR valve vacuum line, which is controlled by the EGR vacuum solenoid. As such, I am assuming it receives vacuum when the
EGR valve does.
As for the two other vacuum lines, one goes into the EGR tube that runs between the exhaust pipe and the intake manifold. The other goes into the exhaust pipe opposite the EGR tube connection.
My guess is that when the device receives vacuum, it opens up a the 1/4" line running from the exhaust pipe (acutally end of exhaust header) to the EGR tube, possibly to help feed the exhaust gasses into the intake manifold. Or maybe used to sense exhaust back-pressure? Not sure.
The reason I ask is that the 1/4" metal tube that was connected to the exhaust pipe broke off, causing an exhaust leak. I fixed the hole and am no looking into tapping a new hole into the exhaust header to reconnect the 1/4" metal line.
In the meantime, just wondering what may or may not be happening while the 1/4" metal tube is feeding fresh air (rather than exhaust) or no back-pressure into the device that connects the line to the EGR tube.
The car also just passed NJ state emissions inspection a few weeks ago, but failed for the exhaust leak. Seems like whatever is affected did not have an impact on emissions.
Thanks! Matt
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Matt wrote ......

Sorta doesnt compute in my pea-brain unless the thing is a differential pressure sensor vacuum modulator for the EGR valve actuator.
That would mean it gates atmosphere based on differential in the tube and manifold.
Whatever .. just put the new hole as near the old as you can get it.
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I took another look at the vacuum diagram and chilton manual, I am pretty sure it is a "backpressure variable transducer", or BVT. Seems like the same thing you described. Still not entirely clear how it works, but yeah, someday soon I plan on putting a new hole near the old one. I think it is a 1/8" or 3/16" tube. I will probably tap a new hole and use a flared elbow and flare cap.
Thanks! Matt
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