I am assuming you realize that if you have the auto fan sw pressed , you will not have high fan until the coolant temp is warm if using Defrost position.
The true test for fan speed of high is to push Defrost plus Max Fan..
That gives you full fan regardless of any other temp wheel settings or coolant temps and this is the Control Panel position you want to use for fan high speed testing.
If you use Defrost plus Auto, you will get low fan until coolant temps increase.
If you use Defrost plus Min, you get low fan regardless of engine temp.
I am sure you know this , but just to be sure.........

Thats a good question. But there is a difference in the power voltage, in engine off mode you have approx 12V, but in engine on mode you have close to 14V. If this is causing the blower regulator to somehow malfunction and reduce the current to the motor, so that the power dissipated as heat can be reduced.

One way to test if this higher voltage is causing the problem is to add a power resistor in series with the blower regulator power. With an appropriate power resistance, you would be able to drop the voltage to about 12V at the input of the blower regulator. I think the current drawn by the blower in high speed is approx. 8A (someone else should verify this also), so to drop 2V, you would need = 2/8 ohms, or 0.25 ohms. The power rating on the resistor would be 2x8 = 16 Watts.

In otherwords, connect the control and ground pins from the terminals on the firewall connector (male) directly to the blower regulator connector (female). Connect the power pin on the firewall connector to one end of the resistance and connect the other end of the resistance to the corresponding terminal on the blower regulator connector

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Saumil S. Patel