There should be a quick initial drop (to the 40-46) as soon as the pump stops so you probably have an issue with your gauge connection. That is often an issue.

It would be good to get the gauge reading properly and then leave it hooked on until you get a no-start so you can have a better idea of what's going on but if you are having good success with the jumper then there is a good chance that the problem is the relay so you just try that since you have it coming anyway.

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1988 325is (purchased new) sold
2004 X5 3.0 2005 X3 2.5
2008 X5 3.0 (new to me)