For there to be current flow, there has to be a voltage differential. If the battery can achieve the float voltage, there will be no current flow. Generally float voltage is set just slightly above the "full" battery voltage.
At a float voltage of 13.4 I see a float current of 300 mA when the four GC2 batteries are full. Is this charging the batteries? Not really. Some counteracts self-discharge. A little is converted to heat and the rest is electrolysis.
The higher one sets float voltage above battery full voltage, the more current draw will be seen, but the batteries will not be charged to a higher state. There is just more heat and electrolysis.
A Trimetric or any battery meter will register the current going to the batteries but is not smart enough to know that some is "smoke up the chimney".