Try this. Turn off the breaker for the outside unit. Activate the thermostat in the house and have someone outside listen to see if they can hear the relay clicking in and out. (noticeable clacking noise). If nothing is heard then probably a bad thermostat. Also, it would be cheaper to go to Home Depot and get their cheapest thermostat for a test than to call out a technician. If that cures the problem then get the thermostat you want.

I wish it were that simple Mike & Tiger. There is no AC brand that is more reliable than another. So many factors go into play here that it would be impossible to come to any 'realistic' conclusion. I see break downs of every single brand, 1yr old, 2yr old, 5yr old, 10yr old doesn't matter. I will tell you I mostly sell Goodman and ICP branded equipment. There is nothing wrong with either of these brands. Goodman is made in America, ICP is made in Mexico. It is what it is. Part of my decision is part availability, the other part is distributors who often challenge warranty claims and give me nothing but hassles to claim warranty parts. If someone requests one brand over another I do what I can to get them what they want. If I have a distributor that doesn't give me any grief with warranty claims or as in the case of Trane --- exclusivity when their product isn't any more special than anything else and they have proprietary parts on most parts of the unit... so when that unit breaks I am putting my customer down to wait on parts. Who wants to pay a premium for equipment only to be with out AC because the parts house is closed when the unit breaks down? Parts houses are only open around 8-5 and sometimes of the year 8-12 on Saturday. You want to pay a premium for equipment only to have to wait around for parts when the unit breaks? (it will break) Go to this thread... I posted toward the bottom showing reviews of most major brands (links within the post) Major Brand AC Consumer Reviews I track breakdowns of equipment I have installed. I typically pay more attention to serious break downs like leaking coils, compressor failure etc. Because these types of failures cost me money to my bottom line. Since I started my own Company (2008) I have not had a single compressor failure on any Condenser that I have 'originally' installed. I have had roughly 6 coils fail within the warranty period of the coil. I would say in terms of percentages probably around 3% of the equipment I've put in. (I do all the work myself, no subs, no installers.) National average for this figure is likely 25-35% or worse... because when I worked for national HVAC company anytime this figure hit above 25% at that company we were scolded to slow down and do more thorough job. I've used multiple brands thru the years, but switched to Goodman and ICP because of better part availability, easier warranty returns with nothing really preventing me in terms of "exclusivity" nonsense. With that said... nothing is perfect when it comes to HVAC.

weedmeister - Thanks you so much for the help. Just to follow up on that's going on in case you're interested" I also contacted Ecobee support a few days before I posted here. I was worried I wasn't going to hear back, which is why I posted here. But it just took a while. Now I've been going back and forth with somebody helpful at Ecobee. The Ecobee guy sent back the same wiring you did, except that he said I can't double-wire the transformer into the Rc and C contacts as you suggested. I did try wiring it up both the way you and he suggested (although without the Transformer), and confirmed the Mini Split would not provide power to the Ecobee. He then suggested it might provide power it I re-wired it using the "O" wire, but it still did not. At first he said that to use the transformer for power, it would need to be done through an Isolation Relay https://support.ecobee.com/hc/en-us/articles/227874527-ecobee-thermostat-installation-with-an-isolation-relay But he later updated that to say I can't use that method because then the Ecobee would send power out to the Min-Split. I actually don't think this is a problem - my reading of the Dry Contact manual is that that's why there's a "volt" switch in it - it's to set the Dry Contact to be OK with power coming into the Dry Contact from the thermostat. I'm hoping I'll hear back from him confirming that, and I can buy a relay and wire the transformer into the Ecobee that way for power. If it turns out that I really can't do that, then I do have an option of running new thermostat wire up from the oil furnace that so I can get another, powered "C" wire that way. Thanks again. Oh, and MiniSplit Heat, thanks for trying to help, but I don't understand how your comment answers anything I asked in my post.

Condenser fan is outside at the compressor. It does not turn on if a thermostat Fan On setting is engaged ... unless the compressor is also running. The evaporator fan is inside, at the air handler / cooling coil unit. It does operate via the Fan On thermostat setting.