I haven't worked on an e34 but had similar problem with e36. On my car the pump and sender have separate wires. There are four wires in the plug - two go to the sender and two to the pump. I suggest you double check the pump connection since I agree with what BMR LVR said. If you have power to the connector and you know the pump works then it should run. From what you describe I would suspect the relay. If it works with the terminals jumped as BMR LVR suggested then the relay is bad. I would use a fuse on the jumper for the relay just in case you connect the wrong terminals or if there is a short somewhere. Good luck!
94 318I, 96 740IL, 97 528I, 07 335I