Fluctuating Alternator output

[motoxxx3]

Having a big problem with my 09 Yaris (at least the Toyota dealer is)
I first noticed my heater blower speed slowing down & speeding up on it's own. It does not do it when I have the exterior lights turned on.
Took it in to Toyota and to cut a long story short the problem is not with the blower, but with the electrical system. A Toyota field tech diagnosed the alternator, as it was fluctuating output in sync with the blower fan speed slowing/speeding up.
They fitted a new alternator & it did not cure it.
The car is now back with them.
I have read about similar problems on here, but nobody has posted the outcomes of what the problem actually turned out to be.
Help!

[why?]

i remember someone mentioning it and the dealership replaced the entire wiring loom. There was a missing/bad ground.