I want to confirm that electricity is not flowing through the unit and it is safe to touch the unit.
I would check for voltage, not current. Even if no current is flowing, a dangerous voltage could be present that would kill you.
Set your Cat III meter to the 600 V AC range marked "V~". Put your black lead into the "COM" socket on the multimeter and the red lead into the right hand "V" socket.
Don't do anything if there is water on the floor or elsewhere. If possible wear gloves - even typical thin synthetic woven work gloves will give a small amount of protection.
First check your meter by carefully probing a known live outlet and ensure it shows the appropriate value (230 or 120 etc depending on where you live)
Second, at the main panel (consumer unit) turn off the circuit for the ceiling light and carefully probe the two ceiling light connections. The meter should read zero.
Third re-probe the known live outlet - this is to make sure your meter didn't fail between the above two steps giving you a false reading of zero.