there's a combination of things that tell the water pump to run... I believe on your car there is also a sensor that turns off the pump or doesn't turn it on until the water reaches a certain temp so that it doesn't just blow cold air.

If you can't hot wire the pump and make it run then you are looking at replacing it. I do not know if the one from Fastlane will fit but you can call teh 800 number and Phil will help you out finding the right one for your car.
I had heard that if the pump stops working it can cause problems with the other electrical items in the heat circuit so I'd suggest you find the problem before running it too much. As to heat when you are driving I thought that the car would be anble to produce enough flow without the pump but I could be wrong. Might be other sensors are staring to go also and that is why you can't get heat when running down the road.
Unfortunately I am facing many of the same issues as my servo has stopped funtioning. it will not open the water valve to let water to the heater core...

Good luck and I hope all this helps in some way.

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'99 S420 - Mommies
'72 280SE 4.5 - looking to breathe life into it
'84 300SD Grey - Sold
'85 300SD Silver - Sold
'78 Ski Nautique