When parked even with the ignition key out and even with the fuel pump relais disconnected, every now and then the fuel pump is on for a couple of minutes (or longer). What would be the logical steps to diagnose ? The car runs fine otherwise.

 

Check (and most likely replace) the Oil pressure sending unit located near the oil filter . This device not only sends a signal to the oil gauge in the dashboard , it also runs the fuel pump at anything over about 5PSI oil pressure . Yours has gone partially shorted across the contacts that run the pump , and is randomly making and breaking the connection .....

 

Last year i replaced an oil pressure sensor because the gauge in the dash went nuts. Is it the same one or the other next to it? The gauge in the dash is still ok.
The one i replaced is a sensor and the other one is a switch, wright? So it'll be the switch i have to replace.
No other things to check, like the pressure regulator ?

 

OK,think i sorted this out. The one i replaced last year was a 1-pin connector. Now the 2-pin connector underneath it had its connector filled with oil which was probably causing the bad/unwanted contact. Cleaned everything thorougly and problem looks solved. Don't know where the oil came from because i don't have a leak, so probably from a crack inside the oil pressure switch. I'll replace it to be safe next time i order parts (ordering just this parts would cost me 5 times its value on shipping and taxes).Thanks Init4fun.

 

Sorry I missed your earlier question , and yes , you have figured it out nicely .

When you have the two sensor system , your most certainly correct that one runs the gauge (single wire) and the other runs the pump (two wire) . The single sender is a 3 wire , which is the one on my car . Funny you mention oil leaking from within the sender itself since that's just what mine did , although on mine it did not affect the pump it did affect the gauge . The oil appeared to be coming from the holes the electrical contacts of the plug stick out from . Please keep a good eye on it till ya replace it because once mine started leaking , the leak grew quickly with use and within a few days use had gotten bad enough to be dripping on the exhaust manifold and stinking of burnt oil everywhere .