Good call, Ed. Most diode testers / VOMs don't put out enough voltage to light up non-Red LEDs.
In the circuit you show the two common cathode R/G LED sets, each with protective diodes to accommodate reversing current flow to determine which color will light up. You have wired them in series with the tortoise motor to control and limit current. However you have wired the two LED sets in anti-parallel to yield Red on one circuit and Green in the other, and reversing their colors when voltage to the Tortoise is reversed. However, the voltage drop to illuminate the Green LED cells is greater than that of the Red. So in one case the Red LED plus the diode across its Green counterpart in the same package is conducting current with a certain combined voltage drop leaving less than desired voltage for an equal amount of current to flow through the other parallel wired set which has 1 diode plus a Green LED. Hence, the Green LEDs will have weaker current flow and may not even light up at all. [LEDs in parallel will not necessarily share current.] Yes, adding an experimental low ohms resistor in series with the Red LED lead may resolve the brightness issue.
Additional ways to improve the usefulness:
1. You could try reconnecting the two LED sets, with their diodes, in series but opposite in polarity with each other and the Tortoise motor. But be aware that the Tortoise motor will slow down.
2. .You could use the LED connection of #1 but use an additional 1K resistor in series with the LEDs, etc. and wire that string in parallel with the Tortoise motor.
3. You could also rewire to connect each one of the LED sets separately, with its own 1K current limiting resistor in series, in parallel with the Tortoise motor.