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We just built a new house and I decided to install an ecobee3 using the same setup that the builder's 7-day thermostat was using. The one exception is I connected up a C wire. It's connected to a single stage Bryant gas furnace.
Current wiring: Imgur
It largely works fine but the ecobee3 doesn't seem to notice when a Honeywell W8150 controller (self-described as a "Fresh Air Ventilation Control") starts the fan. Ideally, I would use the ecobee3 to control when the outside damper opens and closes so that I can take advantage of "free cooling". For now, however, it would suffice to have the ecobee see the fan running. Any ideas on the wiring for that?
Honeywell W8150 manual: https://forwardthinking.honeywell.com/related_links/ventilation/y8150/install/68_0282.pdf
Image of current W8150 wiring: Imgur