I thought that the 4N23 would do exactly the same job as a relay
No it is a transistor not a relay.
What am I doing wrong?
Thinking it works like a relay.
Measure the voltage across the slide projector's two wires. The negative most one should be connected to the emitter and the positive most one to the collector.
Now put the meter on current and measure what it draws when they are shorted ( the current meter is the short ). Is this less than the current rating of the opto isolator's transistor?
Now look at the data sheet, what current do you have to have flowing down the LED to achieve the current transfer you want?