UPDATE:
I've just installed a ground-loop isolator in the Aux jack on the cassette unit to the speaker/amp and it eliminates the hum up to 45% turn of the volume control - which is loud enough atm.
Thinking about the issue, the hum occurred when the amp input jack was connected and the TRS-80 turned on, but without an audio signal in that moment coming from the TRS-80. This is with mono plugs via adapter to stereo amp input.
Earlier the connection from the TRS-80 was mono to a stereo "Y" cable and back to the stereo amp input and through to the mono cassette deck. In this case, the right channel went to "screen" and there was no audio from the rh speaker and volume was lower. Also the cassette deck didn't receive a signal iirc. But there was NO HUM.
Hum only occurred when the mono TRS-80 signal was split/merged via mono/stereo adapter
So although I now have a ground-loop isolator connected; I'm assuming the Loudmouse 2 PC speaker/amp isn't tolerating merging of left and right channels. But the isolator has reduced the effect.