Water should flow at some rate all the time, if only to move engine coolant past the sensors when cold. But if there is no mechanical or electronic thermostat for coolant flow control, the electric water pump may be used for flow control. Yes, 100% constant flow can sometimes work (using fan-only for limited temperature control), but bikes (I think this is for one) have small electrical systems, and electrical load reduction is also fairly important when combined with fuel pump(s), ignitions, lights, fans, etc.
Anyway, I'd see if the Boost Control TPS input can be switched in code for CLT (I don't know), or VVT (non-PID), or perhaps make a little Nano pump control sketch and glue it in your Speeduino case. That assumes your pump is small enough to use with a typical board (about 8A max depending on board trace size and flyback control), or you're going to an external driver anyway.
I'm following this, as there are many interested in using an existing PID output for other stuff like PWM fuel pump pressure control with a fuel pressure sensor, PWM Fan control, etc. It would be great if Boost Control or other feature could have alternative inputs for alternative uses.