As the title says, I keep blowing out fuse 4 and fuse 7 immediately on putting the key in position 2.

If fuse 7 is left dead and fuse 4 is replaced, it stays alive -- fuse 4 only dies with fuse 7 but not alone. I unhooked the whole blower motor and resistor/regulator assembly from the harness, same behavior. I removed and unhooked the automatic climate control module and the behavior stops. If I plug in only the left plug of the automatic climate control, the fuses do not blow. If I plug in the right plug it blows. I bought a replacement climate control unit and the behavior is unchanged.

Nothing new happened to go from fine to the current state, that I am aware of. It was working fine when I parked it, and the next time I drove it (this is my daily driver so it was a few hours later) it started the behavior outlined above. I had a similar behavior about a year ago (fuse 7 blowing) that I did not document or study extensively but it was resolved by replacing the automatic climate control module. This time that did not seem to help.

There's not a lot of other stuff on this circuit so I'm unsure how to proceed.

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'81 240D 4 speed
'97 E420