This happened to me yesterday, and first thing I checked was the relay, found which one was making the noise then took it out. Unfortunately autozone near me does not carry them. So I drove around without the relay to and from the parst store, then when I got home I reinserted the old relay and it stopped buzzing and the ABS light did not come on when I restarted it. I'm hoping it's just a fluke and not gonna come back. But jus in case I'll prob order another relay.
I found this link accidentally, and Hope someone will find it useful, it has the updated modified relay part number. (see below, copied and paste version)
http://svx-iw.com/svxiw/article/print.php?article=16
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ABS Relay Sticking
Author: Subaru
NUMBER: 06-28-96
DATE: 06-11-96
APPLICABILITY: LEGACY, IMPREZA AND SVX EQUIPPED WITH ABS BRAKES
SUBJECT:
ABS RELAY STICKING
Should you encounter the following condition(s) please follow the trouble shooting chart as shown.
The ABS Hydraulic Unit Motor continues to run and/or buzz when the ignition key is turned to the off position.
The ABS warning light comes on and a trouble code "52" for a faulty hydraulic motor and/or motor relay is stored in memory.
Note: It is possible for this condition to occur intermittently. Under these conditions the symptoms may not always be duplicated.
Troubleshooting Steps:
Check if the ABS Hydraulic Unit Motor is running or if you can duplicate the condition.
If the Hydraulic Unit Motor is running, does it continue to run with the key in the off position?
Confirm the trouble code, if any, and trouble shoot according to the Diagnostic Chart in the corresponding Service Manual.
Replace the ABS Hydraulic Unit Motor Relay with a modified one. The new part number is 26735AA012. The new relay can be identified by a white line under the word Japan on the relay case.
Note: Always check the part number supersession for any changes.
If the wiring harness is at fault repair and/or replace as necessary.
The new ABS Motor Relay has been changed in production begining with the following VIN's.
Legacy (SIA built): Sedan: T*206647
S/W: T*308128
O/B: T*374098
SVX: T*100004
Impreza: Sedan: T*510065
S/W: T*810189
Coupe: T*410116
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