How to manually control HVAC without thermostat?
Yes, that's all any thermostat does.  It connects the red wire to one or more of the others to turn on fan, heat, cooling.

The old mechanical thermostats did this with a simple glass bulb full of mercury fastened to a coiled spring.  The temperature  would make the spring length change slightly which would change the angle of the bulb, which would make the mercury run down to the end with the contacts...connecting Red to green (fan) and yellow (in your case, heat pump).

And yes, for your example, most simple thermostats have a way to make the fan run manually...that's all they do.  Hook red to green with a simple switch.  Fan stays on.