Looks that the relay is being powered from a voltage supply elswhere after start up. When pushing the left kicker switch and the 'I' relay staying powered, it seems it does not operate the kick out solenoid or the score motor. Is this correct?
There are 3 x normally open contacts on the 'I' relay bank you need to do some testing of these contacts to determine which contacts perform what task. You can do this by carefully placing a small screwdriver blade between the contacts (to be safe : ensure not to touch screwdriver shaft or wrap insulation tap around the shaft prior).
Here's a diagram to record contact voltages and wire colours which you may want to post when completed for Ian to make comparisons with his machine. (I'm thinking that some wires may have been changed over in the past).