Intermittent no crank?

(Okay, auto parts store electrical system test okay, has a new agm battery.)
Turn the key on, everything works, all lights are on the dash, gauges sweep. Turn the key to start, doesn't crank. The starter does not click. With a voltmeter battery is at 12.8-13.2 volts. I have tried neutral, run through gears, no change.
Now, it will start if I get another vehicle and jump it. Turns over and starts right away. Then throughout the day Turn it off, it will start. But you never know when it's going to not start again. Come out from the store, and it won't start. I've had it start in the mornings also. Seems like it doesn't matter how long it sits between it starting and not starting. I also tried unhooking the battery when I turned the car off. Sometimes it will start, sometimes it won't. Unhooking the battery does not guarantee it will start.