Hi Sydo and good to hear you got it sorted.
Had your shagged battery dropped a cell. As this would explain why your LED lights could only work once you revved the motor.
With a dropped cell, if it was shorted internally, the shagged battery would pull high currents and at idle, your alternator was probably not producing enough current to over come the current draw of the shagged shorted battery.
In any DC circuit, if the current draw exceeds the current supply, the voltage of the circuit will drop.
In your case, with the alternator at idle and not producing enough current, the voltage automatically drops in the hole circuit.
This would account for the LEDs not working and your isolator turning on and off ( this is common and is called oscillating ).
When you increased the revs, your alternator was able to produce a higher current output so the voltage was able to rise, and this voltage rise allowed the LEDs to work.
So yes, what the sparky told you does make sense.