I was replacing my 2 thermostats controlled by a 2 mini zone system (Trol-A-Temp). One of the thermostat has 6 wires/terminals (Y,W,R,G,O,B). The other one has 3 wires/terminals (Y,W,R). I was planning to use an ecobee thermostats but don’t know where to connect the terminals O and B of the first thermostat. Also if I will only connect the 3 wires of the second thermostat, will it be able to access the fan when there’s no wiring provided for it? Thanks.
You'll need a different zone board for this
The bad news in your situation is that your existing zone board (assuming its the Honeywell/TrolATemp MM-2) is incompatible with the Ecobee, at least without parts to adapt it, because it relies on both O and B being available as separate signals from the thermostat, and one of them being energized at all times. Smart thermostats generally only provide a single signal that's configurable to be O or B, so you'd need a 24VAC SPDT relay to adapt the Ecobee's O/B signal to work with your board.
Worse yet, your goal of fan control in both zones gets thwarted completely by the...half-hearted fan call implementation in the MM-2: it calls for furnace fan when it gets a fan call from the primary thermostat, but doesn't do anything for the dampers, causing fan-only operation to simply send all that circulating air down the bypass and back to the furnace in an endless, useless loop.
As a result, I strongly recommend replacing your zone board with a new board; modern zone boards will handle fan-only calls correctly and also work with standard thermostat controls without the need for O or B wires.