Hi,
That's an odd one because it is the same signal through the G terminal of the thermostat that controls the blower in both modes.
Do this,
Remove the front of the thermostat and jumper the R terminal to the G terminal. The fan should come on and stay on until you remove the jumper.
Let me know what happens, basically if that works then you have a bad thermostat that isn't making the R to G switch in cooling but does it on the system switch, another thing to try would be to run the cooling and leave the fan switch in the ON position and see if it runs.
Let me know
Thanks
Mark.
Reply back either way , so we can determine what is going on. These are just troubleshooting procedures and the info will help.
Journeyman Technician
UA Journeyman Pipefitter , HVAC, Refrigeration, DDC controls. 26 years.Commercial & residential