I'm familiar with two types of electric fuel pumps.
The ones used on motorcycles use a spring loaded diaphragm to push fuel toward the carburetor. When the diaphragm gets to the limit of its travel it closes a set of points activating a solenoid that pulls the diaphragm back against the spring and drawing in a fresh charge of fuel. Of course when the solenoid pulls the spring back the points are opened and it quits drawing power. These pumps make a "tick, tick, tick" sound when fuel is flowing. This sounds like what you might have and you're seeing the needle bounce when the solenoid is energized. I can imagine they draw a lot of power when they energize.
The pump I put on my old lawn tractor seemed to be a vane pump. It just made a whirring sound whether fuel was flowing or not. That type would run continuously and so there wouldn't be much change in power draw for the ammeter to register.
Another thing that will come into play is damping on the gauge. If there isn't damping it'd bounce all over the place just from the tractor vibration. I suspect most gauges, at least the inexpensive ones, are damped by just the bearing friction.