Thanks Crater, you are correct, it's a series/parallel switch (On/On). I replaced it last night and it didn't resolve the problem. Could something be wrong with the pickup? There are 4 wires connected to the pickup via the shielded cable. Black, brown, red, orange. If I were to put an ohm-meter to the wires, do you have any idea what resistance values I should be looking for? Or at least to determine if a wire is broken ? Also I am not clear which two wires to put the ohm meter leads on.
It has the symptoms of a failed pickup but dont give up hope just yet. You need to know exactly what model pickup you have. If I remember correctly several versions were used for the RSB Deluxe. Also, keep in mind that it might have been swapped at one point. What year was the bass made and what does the pickup look like? You need the serial number. What does it say on the headstock exactly? RSB Deluxe, RSB Deluxe Special, RSB Deluxe Series, etc?
Once you know the model, you an find the manual or spec sheet for it which will have the ranges for the resistance. A good place to look would be the catalogs where the pickup specs are listed. The readings can bounce around too, especially at first. I have heard some suggest plugging the pickup wires directly into the receptacles on your meter if you have them. Good contact is key. Also, you have to have your meter adjusted to the correct settings to insure a proper reading.
Another thing is knowing which wire combos to test and which component of the pickup the wires represent. You will probably find that some readings are correct, except for one maybe. Make a note of which combo was incorrect. That is likely the combo that your guitar is using when you experience the problems. To know for sure you would have to reference a reputable knowledge base (search the posts here on TB) to confirm your findings. I am sure someone could confirm or direct you to answers if you post your results in the Aria Owners section. I am still fairly new here but it seems like that is the correct place to ask such things.
My guess is one of the coils on your neck pickup has failed. If that is the case, my advice is simply avoid that setting and try to minimize any additional trauma to the instrument. Because you have the dual pickup model, you should still be able to find the sounds you need. That said, PM me if you decide to part it out...

and
never throw a bad one away.
Your other option is to swap the failed one. In that case, I would try to find a vintage replacement that is EXACTLY the same. It wont be easy but it is possible if you are patient. Posting and searching the TB classifieds would be helpful. But IF YOU MUST replace them with new ones made by a "third party", my advice is go with a quality replica such as Rautia or Kent Armstrong so it stays somewhat true to character. Regardless of the results, you have gained some essential APII trading knowledge. Experience is the best teacher..
Good luck Brother. May the force be with you.