Coolant Light turns on when on tiny incline

I'm not 100% sure what you mean by "coolant light". If you're talking about the light on the dash that looks like a thermometer in water, and is red - as far as I know, that's for the engine coolant. Your photos are for the inverter coolant.

You might already know this, but: a Gen1 Prius has two separate coolant circuits. One circuit is for the gasoline engine, just like your father's Oldsmobile. That one includes the coolant passages around the cylinders in the gasoline engine, the mechanical water pump that's on the passenger side of the engine, the two big hoses to the radiator at the front (FRONT) of the engine compartment, and the milky white plastic reservoir on the passenger side of the engine compartment, with the L-shaped "fin" on the top. (This circuit also runs the heater core inside the dash, for heating the cabin and/or windshield, but it's harder to see the hoses for that when you open the hood.)

The other circuit is for the inverter (that big square thing with the aluminum cover that says "Toyota Hybrid System" on it) and the electric-motor side of the transmission. That one includes the inverter, part of the transmission, an electric water pump behind the left headlight, and the milky white plastic reservoir on the driver's side of the engine.

The action for checking the gasoline engine coolant circuit is to let the car sit for several hours without being run. Open the hood and find the radiator cap - it's shiny metal, mostly a circle, with two "ears" on either side of the circle. It probably has a round sticker in the center, and it may have an "ND" logo stamped into one of the metal "ears". It's towards the passenger side of the car, behind the body-color metal that runs across the entire engine compartment right behind the headlights, and in front (FRONT) of that black plastic rectangle that holds the air filter.

Twist that cap counterclockwise about a half a turn to remove it. Look in the hole where the cap was. If there is red-ish coolant nearly up to the top of the hole, it's fine - it's even OK if a little spills out when you take off the cap. If not, go get some Toyota Long Life Antifreeze, either from a Toyota dealer or Amazon. "Import Red" coolant from the car parts store is second choice. Also get some distilled water from the grocery store. Cut the coolant 50/50 with distilled water, pour the 50/50 mix into the hole until it's full, and put the radiator cap back on.

Do NOT use green coolant, like your father's Oldsmobile used.
Do NOT use orange Dex-Cool coolant.

Next, look at the milky white plastic bottle towards the passenger side of the car. It has an "F" mark, with a line, molded into the plastic. If the red/pink color is up to that line, OK. (I like to put my hand on the top of the fender and push on it, to rock the car side-to-side a little, so I can confirm that the liquid sloshes around inside the bottle and I'm not just seeing a stain from where the liquid used to be.) If the red/pink color isn't up to that line, pull the black plastic cap with a hose on it off of that bottle (it just pulls up, it doesn't turn), pour the 50/50 mix into that bottle until it's up to the "F" line, and then snap the black plastic cap back on.

If you had to add coolant to either of these places, then also do this: the next time you drive the car more than 10 or 15 miles, when you get where you're going, turn the temperature dial on the dash up to max (over 85 F), turn the blower to high, and let the car run for a few minutes like that. The heater should be blowing warm air inside the cabin. Once the car has cooled for several hours again, recheck both the radiator cap and the reserve bottle - you may need to add a little more coolant.

If the coolant is always low when you check it, you may have some other problem, like a leaky hose, leaky radiator, leaky head gasket, or leaky heater core.

The action for checking the inverter and transmission circuit is to turn the ignition key to "ON" without starting the engine. Pop the hood and take the lid off of the the reservoir on the driver's side of the engine - the one in your picture. Look in the hole where the lid was. You should see a consistent series of ripples in the surface of the red/pink coolant - this means there are no air bubbles in this circuit, and the electric pump is moving the coolant as it should.

If you don't get the ripples, you probably have an air bubble somewhere in this circuit. The procedure to fix this is more involved, involving applying vacuum (from a hand vacuum pump, or biosourced) to both the reservoir and the two nipples on the front (FRONT) side of that shiny square "Toyota Hybrid System" box.