The real crap winds up in the calipers and that is where all the damage takes place..what you see in the reservoir is dis-coloration from the real crap at the end of each line, so you want to bleed off each caliper.

I use a clear platic line over the bleeders and chase out the old fluid with new fluid from the res.

You will see the new clear fluid through the clear line when the old has been bleed off. There is no pumping brakes or any of that stuff..it is just a simple matter pushing the old out with the new [ pressure bleed from res].
Just watch the res does not get too low to allow air into the system..

You will be glad you did it when you see what comes out of the calipers..they get pretty nasty...............

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A Dalton