BMW Repair: 1986 BMW 735i, radiator fan, bmw 735i


Question
I have owned this car for a few days. I have several questions.
This car is in great condition and I knew it had some issues when I bought it. Mechanically it was well cared for but it was used seldom the past few months.
1.The speedometer does not work. I have checked at the rear diff. and the sensor wires and connector looks excellent with no corrosion. What is the next step?
2.This car seems to have electrical gremlins. The "engine oil light" on the left hand side Service display will not go out and  stay out.  Sometimes it off for awhile and then it usually comes on within a few minutes of driving. The oil is at the proper level and I have tried doing a oil service reset. How do I test the sensor and where is it located?
3. The vacuum pump located on the drivers side upper strut mount will run, often for no reason (if I slam the driver's side door).
Or sometimes I just happen to go outside and I hear the pump is running. The act of opening the drivers side door will usually cause it to stop. Slamming the door again will sometimes cause it to start again sometimes not. This is very unhandy and usually causes a dead battery.
4. Interior and dome lights work only randomly when set to the "door open activate" position. They do work if I set the switch to the ON position. Do you think the switch is bad?
5. Doors will randomly lock and unlock. No particular reason, the might click a few times and lock, although usually they will stay in the lock position. I currently have the door lock module under the dash disconnected to prevent unintended lockout incidents. Where do you recommend I start looking?
Also as a background, the brake lining light was on for awhile, even though the brake pads were recently serviced and then the light suddenly went out. (I checked and the bulb is still good)
The power windows will periodically not function, and then mysteriously they will work again.
Today I went outside and the electric radiator fan was running. This was very strange since it was only 40 degrees out and the car had not been driven in over 8 hours.
I have taken apart the dash and looked thoroughly through the dash panel and the wiring looks very good with no visible damage.
That's about all I can think of.
Any assistance you could give on any of these issues would be very much appreciated.

Answer
I first must stop laughing.I know I shouldn't but having worked on these cars for thirty plus years I have heard theses problems so many times.There is many issues that take time to repair(speedo being one)it is electrical so wiring checks will be often.The wires will corroded internally under the casing,the wire will look bumpy.An ohm meter will be a good friend.Is it the oil level light or pressure light?either way it probably is the sensor.The pump noise is the cruise control(further diagnosis required)unplug it under the hood for now.
The lock issue is due to the age of the car.You will end up taking door panels off and lubing all moving parts.The metals corrode.Once all are lubed then it can be retimed with each other.
The rest of the issues deal with checking grounds and wires.Buy your self a good repair manual with a wire diagram of the vehicle( a Bentley manual ...about $100)