In terms of amps / volts the pump actually sees, you might want to start with that first. Voltage going from the battery, through a switch, through smaller wires and to the pump could see a significant drop in voltage.
It makes sense that your pumps would run no problem straight from the battery, there is essentially no voltage drop.
In terms of current needed by the motor when running, the motor does not require too much. However in terms of locked rotor current, the level of amps needed to break the rotor loose (impeller vanes inside the pump housing) can be up to 10 times higher. (thats why your lights dim when your A/C unit starts up)
The motors in these pumps dont have much giddy up in them to help them from a dead stop. Any degradation in the power supply simply will not break the rotor loose (pump vanes) and the pump will remain locked up.
When my factory impellers failed, I went to install new ones and took note of the very small wire running from the ballast switch to the pumps themselves. Think of the wire as a hose. The bigger the wire, the more current that can pass through them.
In terms of the pumps starting in one rotation but not the other, that may be a factor of where the rubber vanes are and in which direction they are pointed. Breaking them loose when they are pointed in the wrong direction requires more starting current.
Good luck with it.
91' Maristar 210.