BMW Repair: brake pedal vibrations, tank area, 1991 bmw 318i

Question
its a humming vibration and it happens when you turn the key one click without stating the car the noise seems to be coming from the abs motor wich iv just replaced with a second hand part..
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The text above is a follow-up to ...

-----Question-----
hi i already asked this question but i left out that this problem is occuring when the car is stationary i own a 1991 bmw 318i and when i turn the key i can her a vibration and when i press my foot on the brake pedal i can feel the vibrations and they get louder.this happens every time i start the car and it stops after 5-10 seconds
-----Answer-----
Hi David,
Thanks for the additional information, but I need more.
When you turn the key and hear the vibration---do you mean start the car or just turn on the key? Same question when it stops after 5-10 seconds. Is it some kind of clicking or humming vibration? Is the heater turned on?
And approximately where do you hear it coming from, front or rear of engine compartment, rear/fuel tank area, left or right, top or bottom?
I can make guesses based on incomplete information but I do not think it would help you.
Regards,
Tino  

Answer
Hello David,
Thanks for your new info update.
There are 4 possibilities all related to your ABS system:
a) if your ABS pump is part no. 34511157011 (not 34511090427),
remove the plastic cover on top of it (if it is still there),
and you would find 2 relays--- relay for timing/valves P/N
34511157427 and relay for electric drive P/N 34511157426.
One or both could be bad and sticking and this is the most probable cause of your problem. I would suggest replacing both.
b) Or, the pump you recently installed is also bad
c) Or, bleeding was not done properly after pump replacement. Bleeding should be done the old way (with somebody pumping the pedals and another bleeding the wheels) in this sequence-- rear right, rear left, front right, front left. Vacuum and air pressure bleeding in this case is wrong and should not be used.
d) Or, the control module is bad. If you suspect this, with the ignition key off, remove the cable connector to the ABS control module for about 10 minutes, then reconnect. Sometimes, re-booting does wonders, sometimes not.
I hope that I have helped you on this. Please remember that brake systems are safety related  and should be repaired only by qualified personnel since it could potentially be dangerous to occupants of the vehicle or to other people.
Take my advise at your own risk (I am saying this to protect myself from any lawsuit brought about by people doing faulty repairs on safety systems while following my advice, whether my advice is right or wrong).
Tino