Check the wiring to your coin switches. Since they do not have diodes a stuck coin switch can cause weird matrix problems. Cabinet switches are not shown on the playfield matrix schematic. I like to pencil them in along with the tilt and slam sws. That makes it easier to trace the matrix and find the bad switch/diode.

Are you familiar with how to run the switch test on this era of machine?

I think you are on track in your thinking. I cant recall if the white rollover scores some small amount of points, but if it is supposed to then you could check to see if dropping the target scores an odd amount (ie 3,010 points).

I also recall that a ball that sneaks into the collect saucer from the jet bumpers while the gate is already open would not close the gate when the ball is kicked up and out. If a ball dropped in from above the gate would close. It might have been a setting but if its not then your issue might be a little more complex.

Good luck

I love solving matrix puzzles. So to summurize, The saucer rollover button is located at the intersection of ST3-I0. We are looking for a path that will get us from St3 to I0 through the bottom side drop target.
so lets follow the map for the easiest path. We need a shortcut through a target or switch that it's normal to be stuck closed. Coin switches are often the culprate because they do not have diodes. However a drop target with a bad or shorted diode will do the trick too.

Here is what I came up with, start at St3 pass through the spinner then onto St4 via the top side target.
So my scenario is: If the spinner is spinning and the top side drop target is down and has a bad diode then knocking down the bottom side drop target will give you the saucer rollover button. Not an easy path but possible.
Look for your own path from S3 to I0. Remember to pencil in the slam, tilt, and coin switches as they are part of the matrix too.