That is normal. When in RUN, the PCM primes the pump for just a couple of seconds and switches off the relay until you turn the key to START and stays running. Instead on a meter, use something that draws some amps, like a headlight bulb, to see if enough amps go through the wiring. It can happen that you can see a no load voltage but drops off with an actual load. When plugged in, do you hear the pump run while it's priming?
That's pretty low voltage while cranking. Is the battery good?