I'm only a DIYer so take this with a pinch of salt. But you'll see on your pump there's a sensor on each of the hot and cold sides of the pump to detect water flow, with the idea being that when you turn on your shower water will begin to flow (just because of the positive water pressure from your tank in the attic) through the pump, the sensors detect this initial flow and tell the pump to start. So in your case the things that could be wrong are that the flow sensor on the hot water side is faulty or the board on the pump that the sensors connect back to is faulty.
It could also be that there isn't enough positive water pressure from the hot water thank to begin the flow through the pump, if perhaps a valve were closed or partly closed, though you'd think if that were the case you'd also notice that the shower would not be getting enough hot water once you do get the pump running?
It looks like the flow sensor on your pump could potentially be replaced without going near the water in the pump as it seems to just strap onto the pipe, so may be achievable as a DIY electrician job (depending on your comfort with mains electricity). Though a decent plumber would probably have the tools to test if the sensor is the issue, whereas you'd have to just start buying parts and try them out.