Finally we got fixed this mysterious issue. Here is our troubleshooting and fixing know-how for folks in the same shoes:
- the red and orange warning lights came up for us after the hybrid (traction) battery got utilized without proper cooling, i.e. the inverter overheated, because its coolant pump was weak or faulty
- we could trigger the issue with running the air conditioner at max for ~20 mins (while the car parked), or ~40 mins driving in traffic at 25°C outdoor temperature
- the inverter overheating error ultimately had shut down the car completely which if happened we opened the hood and let it cool down (~20 mins) and tried to restart it till all the orange warning lights went away. It was possible to drive the car with the red error light (car icon with explanation mark), but it ran in "gas mode" only and hybrid functions didn't work. A repairman said it doesn't damage the car, but do it in emergency only (e.g. get home in a short distance).
- BTW even after the car cooled down completely (e.g. overnight) we were able to clear the red error with restarting the car 3-4 times. Although, if we didn't clear the error and the car was completely cold the hybrid functions did work, but the display didn't show that on the power flow screen.
- we tried to acquire an original OEM inverter coolant pump (part # G9020-58012), but it wasn't possible at the local Toyota dealership here (Canada). However we could find it on the internet for $500+ CAD...
- we bought a cheap aftermarket one for ~$50 CAD from eBay (we figured we can use the original metal console, so we didn't buy the ~$200+ CAD version that contains that metal part)
- labour for changing it was ~3 hrs (~$450 CAD)
- we double-checked the operation of pump in cold state with opening the lid on the top of rights side radiator. The level of coolant fluid is pulsing (suddenly drops and raises back).
- we tested the solution with a ~300km day trip in ~28°C outdoor temperature while the air conditioner was running. Yaaaay! 😀
Hope this could help other families!