In my experience, an automobile with a factory amp requires bypassing the amp when installing an aftermarket headunit that has a pre-amp built into it (typically 35x4 up to 50x4 peak). Aftermarket head units typically won't play nice with factory amp systems. Most older toyotas do not have an external factory amp, so I haven't run across very many. I just installed a new double din unit in my '90 4runner last weekend, a double din in our celica, and I've gone through at least half a dozen stereos in my old '85 pickup.
As others have said, you might be best off finding which wires to do your speakers, and cutting those off the amp, and wiring directly to the deck.
Regardless, pretty much all in-dash units use the same wiring schmatics, and often the same color schemes coming off the head-unit harness itself. There's always a main power wire for 12V straight from the battery, an illumination wire to the battery, "ignition" wire used for telling the deck whether the key is in the ignition and what position it's in, fancier decks usually have a dimmer wire that gets wired into the dimmer switch, a power antenna wire, a "remote-on" switch that is run to aftermarket amplifiers, and then the speaker wires (+ and - for each speaker). There are often other wires too such as for rear camera hook-ups, DVD video enabling to brake pedal and parking brake wiring, and more, but I'm assuming you are not going to this extent.
I have more experience with the much more common (but older) Toyota 2-plug wiring system used on in-dash units with amps built in. The larger plug has the power wires, ground, and front speaker wires. The smaller plug has the rear speaker wires (and one off the top of my head I can't recall but would like to say is the dimmer).
If you still haven't figured out what to do, here's what I'd recommend; go to
www.crutchfield.com (THE automotive audio website) and look for the "chat" button so you can talk to a sales person (or just call them). Explain your situation and see if they either have a wiring diagram available that they can help you with, or if they have an installation harness designed to work with a factory toyota amp. Of all the installation harnesses I've seen, it's always been the two-plug. I even looked up your year on their site and it shows the standard 2 plug system. What may also help is if you go to the JVC website and see if you can download the manual for your unit (assuming you don't have it to begin with).
I've never heard of using a AA battery to test speakers so I can't comment how well that works. You should basically have the front speakers out or at least extremely accessible at this point, so you should be able to tell what wires come from it and where they go into the amp.