Entry & progression
The support level is not the passenger level. 46 CFR 10.107 defines it as performing assigned tasks, duties, or responsibilities under the direction of somebody at the operational or management level. You are not deciding. You are doing — and reporting, honestly, what you found.
Taking over
You do not take a watch by arriving. You take it by asking, and by looking, until you could describe the plant to a stranger. What is running and what is on standby. What is in hand — a purifier stripped, a tank being transferred, a pump on trial. What is broken, what is degraded, and what is being watched. What alarms have come up this watch, and what was done about them. What the chief has asked for, and by when.
Then walk the space before the man you are relieving leaves it. If something does not look right, ask him while he is still standing next to it. Once he has gone up the ladder, the plant is yours and so is the problem.
TIP — Never accept a handover you do not understand "It's been doing that all watch" is not a handover. If the outgoing watch cannot tell you what a noise is, a temperature is, or a level is doing, that is a live item, not background. Write it down and tell the engineer. The rating who says "I didn't want to bother him" is the rating who is standing there when it lets go.
What you do while it runs
The core of the watch is rounds — the subject of the next lesson — and the response to what the rounds and the alarms tell you. Between those, you keep the space in a state you would be happy to be found in: bilges dry, no oil where oil should not be, tools stowed, nothing loose on a running machine, the deckplates clear.
That is not housekeeping for its own sake. A tidy engine room is a legible one. When the alarm goes and the lights dip, you will find the leak in a clean space and you will not find it in a dirty one.
Manned, and unmanned
Many yachts run UMS — periodically unmanned machinery spaces — at night. Nobody is below; the alarms are extended to a cabin and a bridge panel. Two things follow. The space must be left in a condition that is fit to be walked away from, which is a much higher standard than a space somebody is sitting in. And the person on call must actually go, immediately, every time, in the state of undress that implies. An alarm acknowledged from a bunk and investigated in the morning is not a system. It is an accident with a timestamp.
Communications
Tell the bridge. Before you change anything that changes what the vessel can do — starting or stopping a generator, transferring fuel, taking a machine out of service, anything that could affect steering, power or propulsion — the bridge is told first, and told again when it is done. And tell your engineer. You are not being paid to solve it alone; you are being paid to see it, act within your authority, and speak.
WARNING — Do not operate what you do not understand The support level is defined by direction. If you have not been shown the machine, briefed on the system, or authorised to touch it, then do not touch it — however obvious the fix looks. Almost every serious engine-room casualty has a step in it where somebody operated a valve or a breaker they had not been trained on, for the best of reasons.