Can you see water running into the toilet bowl after you've flushed? And it keeps running? That's probably going to be the flush valve on the toilet. Easy to replace, not that expensive.
Can't see water running into the toilet bowl? Do you see water on the floor of the bathroom? Or dripping to the ground underneath the RV? Then you likely have a split pipe, bad valve, or a bad water pipe connection somewhere. Might feel around the piping going to the toilet for drips of water.
The pump is pressure activated. Turns it on if the pressure drops (by turning on a faucet or toilet valve or caused by a leak) turning it off when the pressure reaches 45 PSI. So if there's a leak somewhere, and the pump switch is 'On' (most RVs have a 'water' switch in 1-2-3 places in the RV where you can switch the pump on or off), that leak causes a loss of pressure, which causes the pump to run to bring it back up.