In the Amiga, the HD LED is connected directly to the IDE port's Drive active/Slave present (_DASP) line, rather than controlled by the IDE controller itself. This means it's totally controlled by the CF card or whatever is plugged into the IDE port, and is the reason that CD drives connected directly to the port cause the HD LED to light for a few seconds during booting. Unfortunately there's probably not much you can do about it, it seems the card might just be constantly switching this line. You could possibly cut that line on the CF adaptor but I don't know if the card requires it. Hard drives as a single device on the bus usually don't have a problem if this line is missing, but of course you can't tell when you're reading or writing.
@the_leander
I would imagine it's already the correct way around as if it was backwards it wouldn't light at all - it's driven by a PNP transistor to reverse the active low _DASP signal, so the polarity isn't reversed to turn off the LED, power is simply cut from it.
*Disclaimer: I'm only this familiar with the A1200 - other Amiga models may be different...