I am trying to hook up a honeywell round thermostat to a simple computer fan. I can get the fan to run continuously or not at all. Currently, the red fan wire is connected to the G terminal, and a white/black wire from a wall adapter is connected to the R terminal, which is bridged with Rc terminal. The fan will run when I connect the black fan wire to the black wire from the wall adapter, but only if the thermostat is set to "fan-ON", the auto setting will not work?
Any ideas what I have done wrong? There are a total of seven terminals, R, Rc, O, G, Y, W, B, I believe.

What type of computer fan?

Unsure of brand, but it's a three inch fan, I think it's rated at 12 volts and maybe 200mA, has a red wire(positive?) and black wire(negative?)

How are you powering the fan?

Are you trying to bring the fan on at rise of tempature?

What happens if you switch the thermostat to cool and lower the temp on the dial below the room temp. With the fan switch on auto.

I bridged the connection between Rc/R and W or Y, can't remember which right now, and I think it might be working properly. My garage is so hot right now that it is above the max temp on the stat, and I have to wait until morning to see if it is working properly.
I am powering it with a 12 V DC adapter.

Hvac, when I switch the fan to auto, it just keeps running, but I think it may eventually shut off if the air temp cools down, it's just a test run right now and the fan itself can't cool the air . It's all part of a cooler system that uses jugs of ice to chill the air, and I have been running it unsealed, so there is no actual cooling going on.

The connection from "Y" to Rc is what you need to run the fan in cooling mode.
Connecting to the "G" terminal will enable the fan to run or not run by the fan switch only.

Watch the humidity moist air is a conductor.