Help!! Fender Jaguar bass seemingly possessed...

I had something like that happen with a loose connection once. I never did figure it out, it just stopped on its own. Good luck.

 

Preamps are as individual of a choice as preamp pedals, pickups, even the bass itself.
Me, personally, I dig me a John East U Retro every time. They're solid, give you a variety of tone options, including a mid sweep in most cases, and can give you basic operation if you unexpectedly run out of battery.
The new ones are even more tweakable because they have internal trim pots.
There are lots to pick from. Best Bass Gear.com is a good place to start looking.

Hope this helps!

 

Indeed, I believe your preamp is toast. I had the very same issue in a "Jazz Bass Plus" that I owned. I took it to a tech who opened it up and showed me a small burn mark on the circuit board. It was a really, really sad day because I adored that bass, and it was long out of production by the time that happened, and there was no replacement preamp that would equal it.

 

Fender probably can set you up with a stock preamp replacement. Their customer service folks are super nice and helpful.

Good luck.

 

Did you try cleaning all of your connections?

 

The fact that taking the battery out stopped it makes me wonder about the jack. I think the jack may not be switching off the battery.