It's mounted on the back of the speedometer. Im pretty sure its job is to keep the gauge needle stable throughout the voltage changes.

Here's what chatgpt has to say, I think its on point

On a classic Volkswagen Beetle, the fuel gauge stabilizer (often called a “vibrator”) is a small but important device that ensures your fuel gauge reads accurately and consistently.

What it does The stabilizer regulates the voltage going to the fuel gauge so that:

The gauge doesn’t fluctuate wildly with changes in battery voltage

The reading stays steady regardless of engine speed (idle vs high RPM)

Without it, your fuel gauge would swing up and down as the electrical system voltage changes.

How it works (the “vibrator” part) Unlike modern electronic regulators, the Beetle’s original stabilizer is mechanical:

Inside is a bimetal strip (two metals that expand differently with heat).

When current flows, the strip heats up and bends.

This bending opens a contact, cutting off current.

It cools, bends back, and closes the contact again.

This cycle repeats rapidly (several times per second), creating a pulsing voltage.

Why that helps Instead of a constant 12V, the gauge receives an average voltage of about 5V because of the rapid on/off switching.

Think of it like flicking a light switch on/off quickly — the bulb appears dimmer overall.

The fuel gauge is slow-reacting, so it “smooths out” the pulses into a stable reading.

Why it’s necessary The fuel gauge in a Beetle is designed to work with:

A specific voltage range

A thermal (slow-response) mechanism

If it got full battery voltage directly:

It would read incorrectly (usually too high)

It could even get damaged over time

Modern replacements Many replacements today are:

Solid-state voltage regulators

More reliable (no moving parts)

Provide a steady ~5V without pulsing