Well, I’m not sure what’s happening with the LED/motor combo, but the open drain output means that the TC54 can’t go ‘high’ to turn on the NPN transistor. (edit: although, why does the LED blink? -scratches head-)
You can get a TC54 with a complementary output, like in the 1381, but maybe do an experiment and try a 100k, or maybe even a 1Meg, resistor from the base of the NPN to the +ve of the circuit. Hopefully it might act as a ‘pull-up’ to get the solar engine firing.