Testing with a 50Hz sine source of 12VAC (No scary mains here), it takes a current of about 300mA to start to register on the 71D Amps range, otherwise the display shows 0.0 amps. So it looks like your meter behaves correctly. Accuracy is not there though and it is probably better to respect the 10% of range limitation (1A). At 500mA, it still overreads by 20mA, but frequency is correct.
The Fluke and Gossen agree with each other on the Amp range.
No funny beeps on the 71D.
The Gossen's accuracy is also only valid for 10% of range or more, but it has a 3A range.
The Fluke 185 has the same 10% of range limitation on its 5A/10A ranges.
Probably all to do with the true RMS converter.
Ideally, the 71 series should have had a 4A AC range, to prevent a wide gap between 400mA and 1A.