There is no manual gas valve to the heater. The gas valve is controlled by the heater circuit board as needed.
The fault light means it attempted to light but did not succeed. Not necessarily anything more than a gust of wind, but could mean dirt or an insect nest in the burner feed tube. Just turn the heater switch off and on again and see if the problem persists. This is probably not your original problem with intermittent hot water.
Your not-so-hot problem is almost surely caused by cold water mixing with the hot somewhere downstream from the tank. Typically this means a valve is open, e.g. the shower hot & cold are partially open with the water turned off at the shower head, or the heater bypass valve is partially in bypass mode. Your heater bypass valve appears to be in the open position (parallel to the line) but we can't tell whether it should be open or closed to be in bypass mode. A picture would help, or you could just try the other position. Another common problem with a single valve heater bypass plumbing is a failed check valve where the line exits the heater. It is not unusual for the hot water exit check valve to get stuck due to crystallized mineral salts in the hot water. Check valve replacement may be necessary. You said the trailer is new, but has the heater been in use long? Hard water can take a toll on plumbing!
Last, do all hot water faucets act the same? Try each one and see if any are OK.