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Only a matter of a few cranks of the starter, but enough to know there's something not right with the fuel delivery. '79 starts with maybe 3, 4 turns, the '81 needs noticeably more.

Any guidance for where to look, swap out first ? Seeing the in tank fuel pick up, filter post, the '81's has not been out in my 20 years owning. The exterior pump, hoses, filter yes.

Fuel pressure regulator, sensors, now I'm into the not knowing how to test, procrastination, aversion zone to require just checking the wiring connections and swapping in another part for comparison.

Some seem to take 3 compression cycles, some 6, but since the injectors are batch fired I doubt it will ever be less than 3. I'd start with residual fuel pressure, hook up a fuel pressure gauge and let it sit overnight, then check pressure before starting. Backtracking a bit, I'm assuming you mean it's a little slow overnight, not a hot start after a trip to the store.

Ditto what Mike wrote. Get a pressure gage at the hardware store along with a 5/16 barbed adapter. Take the line off the cold start valve and plug it in there temporarily. Make sure to use a hose clamp.Crank the engine and watch the gauge. Careful when you detach the line because fuel will probably spill.

Do my homework, to know what fuel pressure gauge, number spread or yes there is pressure, no there is not, to buy. I do that anticipating counter clerks might not know.

Figure out how to connect, using barbed adapter, on the end of the cold start fuel line using a hose clamp.

Crank the engine. Then from what I see on the gauge, an as yet to be determined healthy or sick number, or yes there is pressure,... there must be, it starts but not as fast as it should.

Then I will know something about the fuel pressure off the end of the cold start valve. I will post that. And if the problem is overnight cold and/or warm...

And ask again what to check first: Fuel pressure regulator, in tank pick up, sensors, the part most likely needing replacement or cleaning to fix the slow start problem.

I wouldn't put the gauge on old hose, too much risk it will crack when you don't want it to.
Check all the hoses at the pump & filter, they get brittle.

Pressure:3bar or 43 psi
Make sure the gauge is rated for gas
With key on, engine off, pump should Turn on and supply full pressure.
With key off, wait an hour or more annd recheck pressure; should hold. If not, you have a leak in lines or in pressure regulator. Check for wet spots, most likely at connjnections of hose to hard pipe, mine was at top of tank fitting where line was squishy rotten. Check injector hoses too. If hoses and fittings are good, pressure regulator is most likely culprit. My car never sat for any extended length of time so houses never had a chance to harden.
Have you done a recent filter replacement? Could be the filter is slowing things down.

86 views, the motivation for posting the erstwhile solution, answer to my question applying to my specific 1981 BMW 528i not starting quickly.

The shortest distance between two points being a straight line, my logic and being lazy chooses asking questions of the FirstFives experts. Sometimes their answers provide the quick fix my lack of education is seeking. Sometimes, no offense, I must realize their experience and knowledge accumulated over the years,... has forgotten how uneducated I can be. To include asking for a solution to a problem omitting the list of important variables such as the condition of the fuel lines, filters,...

Thank you gurus, I intend to purchase a fuel pressure gauge and keep your instructions for use.

My solution, deductive reasoning, take a shot at replacing the cold start injector,... not injecting enough fuel. Just do it, see what happened. Maybe dumb luck, that worked. The engine starts cold now, quickly.

On a roll I returned to the challenge of inserting a flat blade screwdriver into the brass throttle body idle adjustment screw. Left, right, listen.

Whatever I did, the dang contraption starts right up and idles lovely. Until it doesn't or the next thing falls off.