Dusk to dawn light goes out when heat pump starts up
I am pretty sure what you have is classic case of voltage drop. Ballasts for vapor lights and some cheap light sensors for incandescent par bulbs will be tricked or drop output, so light goes out and has to restart when voltage is restored.  The reason for the sudden drop is really the concern.  Since the heat pump employs a fairly large motor, it draws a lot of current at start up. This is called inductive kick. It takes a few seconds for the coils of the motor to saturate and start he armature spinning in the magnetic field. Since the coils are a dead short until saturation is achieved, they draw large current.  E = I/R, ohms law explains this. So what is the solution?  You may need to have the heat pump motor checked out or add a motor starting capacitor across the windings. I cannot tell you what size capacitor you will need as it can vary widely depending on motor size. This is a very common problem in residential services that are close to current capacity with an unbalanced motor load. Even though you may have a 100 or 200 amp electrical service, it can be overtaxed temporarily  by an unbalanced motor start up