Your are right that it disappears down the right side of the car or at least on my '86 anyways.

It goes down and winds along the door sills under body support frame work for the seats. A real bugger to pull out of a junker. They nail that line down with black sticky stuff used along with the wiring harness for other accessories.

You did not say whether you opened up the area in front of the right taillight or not.

There is a tiny right angle check valve in the compartment on that line that fails!

You might want to remove it and then flush the line back to that point.

I think you can just leave it out as the nozzle is up high on the last pillar so it won't drain out but may drain back a few inches.
The check valve just helps keep the line more full so it takes less time to start the spray.

Phil