How to reduce voltage to drive tiny DC water pump?

Keep thinking, because you are really close now!

The open circuit (no load) voltage from a solar cell is mainly dependent on temperature and as Dereck said it will be the same from a flashlight or moonlight or full sunlight. What will vary is the amount of current the cell can produce. That current will be directly proportional to the amount of usable light shining on it. So the current available will vary during the day as more or less light hits the panel.

But for a given amount of light, the panel will deliver close to that same amount of current into a short circuit or a low (thank you Dereck) resistance load. The current coming from the panel will not start to decrease significantly until the load resistor is high enough that it and the voltage are limiting the current rather than the current capability of the panel. So that is the "constant" current behavior of the panel.

When you connect the motor to it, the voltage output from the panel will be whatever it takes to force the current it is capable of producing through the motor. So with the motor connected, you will see the voltage rise as the sunlight on the panel increases. But that is really the effect of the change in available current rather than the open circuit voltage of the panel changing at all.

I hope that has not been more confusing than helpful.

Not a high resistance load. Think about that for a minute. Say you have a 100 watt panel rated at 18 volts and 5.55 amps Imp and 6.2 Amps Isc. The highest resistance the panel the can deliver its rated power is 3.2 Ohm's. If that statement were true the panel would generate 123 watts into 4 Ohm's. At a high impedance of say 1000 Ohms is enough to run a several large luxury homes in Florida with pools in summer and all the amenities at 38 Kw.

I know just a typo. Paybacks are heck huh?

No - it's not confusing at all. In fact, you explained it in such a clear and simple way that I think I can understand it! (Although I admit I need to let this seep in and ruminate for a bit.) Thanks so much.

Maybe if I connect it to a negative resistance load???

Thanks for the catch.

I have a negative resistor for sale. Will turn any energy source into a above unity gain. You can run the world on a flashlight battery. Send my $19.99 plus shipping and will send you the book with instructions and the resistor.