I may be missing something obvious here, but . . .
If all you want to do is move a meter needle slowly back and forth when you open and close a switch, there's a much easier (and cheaper) way to do it.
Power a voltmeter with (an appropriate) DC voltage that's fed through a resistor and the meter terminals are in parallel with an electrolytic capacitor (it has a + or - marking so be sure to match polarities). The values of the resistor and cap will determine how long it takes the meter to reach full scale. At first, the cap acts as a short (closed circuit, so make sure your resistor is large enough to prevent a fuse from blowing), so the meter reads "0" when voltage is first applied, but as the cap charges, it increases in resistance, so more voltage goes to the meter, and the needle gradually rises to report the voltage supply. By choosing higher values you can even make it fast at first, then gradually slower and slower as the capacitor reaches full charge (and looks like an open switch).
When the power is disconnected, the cap acts as a very small short-term battery that gradually discharges through the meter, so it slowly falls from the full voltage reading to zero. Just put a "Temperature" scale on the meter face.
By choosing good values for the resistor and cap, you can choose the speed that the meter rises to full and drops to zero (can be two different speeds). High values will take a long time to rise and fall, low values will make the needle move quicker.
If you want just the fall-time to be faster, put a second resistor in parallel with the capacitor to give it an additional discharge path. Measure the resistance of the meter itself, use the same value resistor, and the meter will fall twice as fast. Again, different values will also affect the rise time, since the extra resistor is now in the rise circuit, as well.
To save time, you can work with battery power to keep from blowing a fuse, and use potentiometers to get the resistances the way you want, and connect capacitors in parallel or series to get odd values. Capacitors work the opposite of resistors -- caps in parallel handle the same voltage, but have more capacitance. Resistors in parallel handle more wattage, but have lower resistance. Caps in series have less capacitance, resistors in series have more resistance. Multiply R (in ohms) times C (in farads, 1 uF is 1/1,000,000 Farad) to get timing values.