I can't tell for sure how many components you have in the outlane switch. Here are some shots from my Apollo (same game but the replay version instead of Add A Ball). Mine has (from bottom), 2 long thick fish tape, long contact, short fish tape, short tensioner, short contact.
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I also have the schematic for Apollo, though I am not sure what would be different on Blast Off to make it AAB instead of replay.

The main thing in the circuit between the outhole and the relay is the small ball (bagatelle) rest switch. Basically the game needs to make sure the small ball is at rest before it will fire the large ball. In other words, the action in the backbox has to complete before the next ball will be ready for play. Here's an image of that section of the schematic.
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The switch should look similar to the rest, I haven't taken a good look at mine. I would assume it would be near the coil launch in the backbox. When the ball is seated, it should be closed, open when it's sent. It's a bit harder to get into the backbox on mine the way I have it setup. If you can't find it let me know and I can try to get a picture. Here are some more images of the Apollo schematic...again, not sure what is different on BlastOff, but I would assume most components are close.

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Here's a pic of that switch (the double right above the coil)...you'll have to take off the back cover, and it's behind the coil linked in the ipdb above.
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For mine, when the little ball is down, they are closed. If I lift up on the plunger raising the ball, they open. I have had the little ball get stuck in the nails before, and it would not launch a ball until the small ball fell back into place.

Also, for the pop issue, as the DR mentioned, there are 2 switches. The top switch with the spoon, in my picture is normally open, and is closed by the post from the skirt when the ball rolls over. This should activate the pop, pulling the metal piece down...the yoke then hits the bottom switch which is normally closed, opening it. This will trigger the relay to switch which bumpers are lit I believe. For testing the coil, on mine (without disconnecting any wires) I was getting between 2.5 and 3.5 ohms on each of the 4. I'm assuming if you are much higher/lower than that it would indicate an issue.

Good luck.

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Too bad this one (or Apollo, or Lunar Shot) haven't been done by bgresto... This might be tough to find a replacement glass.