I have a small 12v N20 gear motor
RPM - 400
Current - .03 amps no load / .1 amp rated load / .72 amp stall load

Torque will all but be negated. As long as the output shaft turns, it perfectly ok for my application.
I'm waiting to hear back from the manufacture on the minimum voltage required to operate it.

So, let's just say the minimum voltage required is 3v, thus in the title. Best would be fixed at the desired voltage. But given how small and the current draw, I'm not sure what's the best route.

 

You can test this with two 1.5V batteries. D size.
I see two ways to do this. One is constant voltage. We can make 3V or some voltage.
The second way is constant current or use a resistor to limit the current. A 300 to 500 ohm resistor will slow down the motor. We really don't know the value right now.
I assume you do not have the motor yet.
I would make the voltage or resistance variable so you can adjust it later.

 

It is scheduled to be here this evening. One other thing I forgot to mention is the timeframe in which it will run 12v will be approximately 7 sec or less and about 2-3 sec at minimum voltage.

And yes, didn't think about that. I actually have a sleeve that holds 2 AA batteries I could use to test.

 

Now a question: Is the running on 3 volts selected to provide a slower speed of the motor, OR is the running on 3 volts due to power supply conditions?? What determines the seven second run time? Is the motor running to a position, or just for a time, with no need for an accurate position?? The simple scheme for the low voltage/slow speed .
It is very likely that once the motor is truning that it will keep turning with only 3 volts applied. MOST DC motors will coast after the power is removed, unless they are short circuited, in which case they will stop quite quickly.
So we really need a more detailed explanation of what is actually the desired operation.

 

12v power supply to system. The 7 sec run time is determined by a programmable 12v relay timer. Once the relay is triggered, 12v will be sent to the motor for 7 sec or so, depending on my time programmed. Once the 7 sec is up, 12v will no longer be sent to the motor. However, a second relay will send 12v to the motor through some sort of voltage regulator and drop the input voltage to the motor down to 3v or so.

This motor has little to no coast down. When power is removed, its virtually a stop.

 

Motors arrived. Checked with my 2-AA setup. Works down to 3v. Tried it with 1 battery and it will operate down to 1.5v and has more than enough torque down to 1.5v.

So now the target is to go from 12v to 1.5v

 

I may have solved my own problem.

I have a PWM (Pulse Width Modulation) controller. Small, but works. I was able to turn it down to .5v dc which dropped the rpms from 400 down to 16 rpms. Infinite control speeds from 400 to 16. I may try this on my project.

 

I have a PWM (Pulse Width Modulation) controller.

That's actually a preferred method because the higher voltage of the PWM pulses result in higher torque at that instant, which helps to get the motor spinning despite the lower average voltage.

 

Also the PWM circuit is much more efficient than any linear regulator in dropping 12V to 1.5V.