I grew up with carburetted BMWs in hot South Africa. The cars would get so hot that the fuel in the lines would turn into vapor, which a fuel pump can’t pump. It only handles liquid. The car then stalls and won’t start until it’s cooled down. This situation is called “vapor lock.” It could be resolved faster by laying cold, wet towels around the fuel lines near the carburetors, but it wasn’t a great situation.
A few years ago, I bought a BMW 735i in the San Diego area, and while driving it up the long incline on the freeway out of San Bernardino towards Las Vegas, the car got vapor lock and stalled. As if that wasn’t bad enough, a few months later I bought a 733i in the same general area, drove it on the same road and experienced the same thing in the same place.
The fuel-injected BMWs of the mid-1980s (and presumably also before and after) are fitted with an auxiliary fuel pump inside the tank, whose task is to keep the lines pressurized regardless of what the main fuel pump is doing. This prevents vapor lock.
If the main fuel pump fails, the auxiliary fuel pump cannot generate enough pressure to keep the engine going. Its only value is in preventing vapor lock.
If the auxiliary fuel pump fails, the fuel can still flow through the pump, so it’s not as if failure of the auxiliary fuel pump makes the main fuel pump fail. But, indeed, the cars are then vulnerable to vapor lock.
To get to the auxiliary fuel pump (a.k.a. in-tank fuel pump) on my 1984 BMW 633 CSi I removed the carpet, and then on the passenger side I found a black round plate attached to the trunk floor with three Philips screws that I removed.
I could not remove the auxiliary fuel pump setup without first removing the in-tank fuel level sensor, which required me to remove four 8mm nuts, each of which has a little washer. With the nuts removed, I could slide the sensor up and out, after I removed its electrical connector.
Then, I removed the six 8mm bolts that held the auxiliary fuel pump attached to the tank, and after I removed its electrical connector and its two fuel lines, I could twist it through some weird angles and pull it out of the tank.
The unit has a large, screened horizontal fuel pickup that’s shaped almost like a foot. It’s attached to a down-pipe that’s sort of like a leg. The pump unit and the various lines & hoses are shaped in the way you’d expect this sort of thing to look like, in order to work.
Finding good used units are likely to be a difficult task. So far, every 6-series and 7-series unit I’ve tested has been bad.