Decrypting the Vado Identity wired shower controller

Monkey3:
Exactly the same. Still HIGH.

Is the MAX485 module in RX or TX mode when you take the readings?

EDIT:
Using the simple test program below on a Mega

#define DE 2
#define RE 3
#define TEST 4
#define DELAY 100

void setup()
{
  Serial.begin(115200);
  Serial1.begin(9600);
  pinMode(DE, OUTPUT);
  pinMode(RE, OUTPUT);
  pinMode(TEST, OUTPUT);
  Serial.println("Setup End");
}

void loop()
{
  Serial.println("DE/RE High");
  digitalWrite(DE, HIGH);
  digitalWrite(RE, HIGH);
  digitalWrite(TEST, HIGH);
  delay(10);
  Serial1.print("Hello World");
  delay(DELAY);
  Serial.println("DE/RE Low");
  digitalWrite(DE, LOW);
  digitalWrite(RE, LOW);
  digitalWrite(TEST, LOW);
  delay(DELAY);
}

I get the below image on my LA. You need to put the MAX481 into receive mode to release the lines.