The cooling test sequence for this board, says to jumper Y & G to R. Make sure the fan comes on, and spins up to the proper speed. Then remove the jumpers, and check the fan off delay.
If the blower does not come on, verify that the COOL terminal is energized. Use a voltmeter between COOL and neutral, and verify 120 volts (with jumpers in place).
If the COOL terminal is energized, check the motor and verify all speeds are working properly.
If the COOL terminal is not energized, the board my be bad.
According to the schematic you've provided, you have a multispeed blower (which is quite common). The speed at which the motor runs, is determined by which wire is energized. Energizing the red wire; for example, will run the motor at low speed. Energizing the black wire, runs the motor at high speed.
Before you disconnected the board, one of the motor wires was connected to the HEAT terminal on the board, and one was connected to the COOL terminal. Looking at the ladder diagram, it looks like the blue (MED) wire was connected to the HEAT terminal, and the black (HI) wire is connected to the COOL terminal.
If you've run the tests described above, and found that the COOL terminal is energized when the jumpers are in place. You can try connecting a different speed wire to the COOL terminal. If the motor spins up with the other wire connected, it means that the original speed is dead or something's wrong between the board and the motor.
It looks like the LO speed red wire is attached to the M1 terminal on the board. I'd swap that to the COOL terminal (just temporarily for the test), and see if the motor spins up when the jumpers are in place.
WARNING: DO NOT run the A/C for long with the motor at a lower speed..
You could use the EAC-1 terminal to power a step-down transformer. This is common with furnaces that energize the HUM terminal to line voltage.
Check the humidifier manufacturer, they should have a properly sized transformer to fit this exact need. They should also have a wiring diagram for this type of setup, in the installation instructions.
Basically, the primary side of the transformer will connect to the EAC-1 terminal, and a neutral terminal on the furnace control board. Then the secondary side will power the humidifier.
Whenever EAC-1 is energized, it will power the transformer, and the humidifier will turn on.
As noted in the comments on the question, you may not get the expected results.
Best Answer
You need to add a relay to the system to independently operate the fan separate from the heat.
The simplest way is to buy a new high voltage 120VAC (20-30 Amp?) heavy duty relay/contactor that switches with a 24VAC control voltage and connect both relays to the high voltage circulation fan. If either relay is on the fan gets power. The existing fan relay will power the fan when you call for heat, and the new fan relay will power the fan when you call for fan only.
If you don't add a relay and still somehow hook it up, your heat will probably turn on every time it calls for fan only.