There are several significant observations to make about the behaviour of the metering shown in the video.
Firstly, all the channels are affected, so that, for example, it's unlikely to be a phantom power problem on any one channel.
Secondly, the fault gives similar, but not the same, magnitude of effect on every channel, and corresponding decay times.
Thirdly, there are not many places in a complex analogue system such as the Amek Angela that have time constants of order 1 minute.
The initial suspect area is the power supply rails, as Paul suggested. I've not been able to find any Angela schematics on line, so a guess would be that the design of the metering section is not proofed against variations in the internal power rail voltages.
A cause of the problem could be leaky reservoir capacitors, or high-impedance contacts at the rectifier diodes or at the voltage regulators. If I were sitting next to the console with its lid removed, I would put a digital voltmeter on the power rails feeding the metering board and see how much variation in rail voltage could be invoked by feeding a signal generator or some loud music through many channels at once.
