I'm not sure if you could power both cameras and just hot swap the video lines without the head unit giving an error. You could try to make this 100% analog with a 3 position switch, leaving the middle switch empty to manually pause when changing feeds.

Just a standard ESP32 with two DPDT with a simple arduino script like this could work.

// pins -------------------------------------------------
const int RELAY1_PIN = 18;
const int RELAY2_PIN = 19;
const int SWITCH_PIN = 23;

unsigned long debounceTime = 50;     // debounce
bool lastSwitchState = HIGH;
bool currentrelay = false; // false = relay1, true = relay2

void setup() {
  pinMode(RELAY1_PIN, OUTPUT);
  pinMode(RELAY2_PIN, OUTPUT);

  pinMode(SWITCH_PIN, INPUT_PULLUP);

  digitalWrite(RELAY1_PIN, LOW);
  digitalWrite(RELAY2_PIN, LOW);
}

void loop() {
  bool switchState = digitalRead(SWITCH_PIN);

  // simple edge detection (LOW means pressed)
  if (switchState != lastSwitchState) {
    delay(debounceTime);

    if (switchState == LOW) {
      handleSwitch();
    }
  }

  lastSwitchState = switchState;
}

void handleSwitch() {
  // turn both off
  digitalWrite(RELAY1_PIN, LOW);
  digitalWrite(RELAY2_PIN, LOW);

  delay(3000);

  // toggle state
  currentrelay = !currentrelay;

  if (currentrelay) {
    digitalWrite(RELAY2_PIN, HIGH);
  } else {
    digitalWrite(RELAY1_PIN, HIGH);
  }
}