Theo

The pause is almost always in the control path rather than the power path, and that distinction is what makes it diagnosable.

When you turn the key, a small current goes to a relay or solenoid, which then closes a much larger connection to the starter motor. Tiny current makes a decision; huge current does the work. A pause with total silence — no click — means the decision is not being made yet. If the big connection were the problem you would hear a click or a heavy clunk and no crank, which is a different fault.

So the suspects are the ignition switch contacts, the starter relay, or a neutral-safety or clutch switch in the circuit. All of them do the same thing when they wear: the contacts oxidise or the mechanism gets sloppy, so the connection is made a moment late, or only after enough voltage builds up to bridge the gap.

Good news for question 3: a battery reading 12.5V and cranking normally once it does go is not the failing part.

"Most of the way, and the last part is the part that matters for battery life" resolves it. Both people were describing different ends of the same curve.

The real reasons to care are about the pump, not economy, and they are worth more than the 1%:

• In most cars the fuel pump sits in the tank and is cooled by the fuel around it. Running consistently near empty means it spends its life in the hot, uncovered part of the tank. This shortens its life, and a fuel pump is a genuinely annoying repair.
• Anything that settles out — water from condensation, debris from a bad fill — sits at the bottom. Habitually running the last few litres means you are drinking from the bottom of the glass more often.
• In cold weather, more air space means more condensation as the tank breathes with temperature swings. This is a real argument for keeping it fuller in winter and roughly irrelevant in a warm climate.

None of that is about miles per gallon. It is about not replacing a pump early. "Do not habitually run it below a quarter" is the useful version of the advice.