You do not ground the wire going to the ECU, you ground the wire going to the FCM. Make sure you are grounding the right "half".
The fact you can cut that wire and not get a light bothers me, that is NOT normal behavior. In fact, I have a switch under the dash that I can use to open the connection, I get the light and the fan goes to ward speed. I use this to keep the A/C super cool in stopped Dallas city traffic. I call it my "instant cool" mod.

That light is either burned out or the ECU has a REAL problem. But again, the fan module should run the fan at high speed anytime the wire is cut. Grounding it should NOT be needed at all. If the FCM dos not see pulses from the ECU, it goes into emergency mode. Let's look at it this way, ya gotta get the FCM to act normally. Sounds to me like your FCM is bad.

Now, again, make sure you have 12 volts on the IGN lead to the FCM. The fan wont run unless you have 12 volts on the IGN wire to the FCM AND on the Big, fat, red wire.