If your fuel pump is old, they do fail and need to be replaced. Replace the filter while you're at it. I have to admit that I don't know if they are supposed to run intermittently or not, but I don't think so. There is a bypass for the fuel so I think it runs continuously. How many miles on the car?

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Steve
1985 Mercedes 500SL Euro (Gray market)
1995 BMW 520i Euro (Gray market)
1992 BMW 525it Wagon
1994 Honda Del Sol Si