Decrypting the Vado Identity wired shower controller

Riva:
AFAIK the 3 characters after MAX485 denote the package type. ESA is 8 pin SO package.
When your testing you only have them connected to the logic analyser?
The Amazon link you posted has a schematic image so maybe check module matches schematic with a continuity meter
Maybe the whole packet of MAX485 modules are faulty or poorly designed/built or it could just be your logic device pulls the lines high when they are floating and mine pulls them low.

When testing, I've tried a couple of different combinations and they all give the same result.

CHANNEL CONNECTED SIGNAL AT IDLE
A arduino and logic analyser high
A arduino, controller and logic analyser high
A mixer and logic analyser low
A mixer, controller and logic analyser low

So I've ordered another, very different rs485 (https://www.amazon.co.uk/gp/product/B07B667STP) which should be turning up tomorrow so, with any luck, this will resolve the issue.