Are you replacing the original radio that had a remote amp, with a radio that has a built in amp? If so, yes you might need to jumper some wires at the location of the amp to allow the new radio amp to connect to the speakers.
I say you might because not sure if Toyota installed wiring for both types of radios, those with and without internal amps in the radio. Once you get the radio out, you will see what wiring is there.
Rather then explain this, go to the link below and find the wiring diagram for this generation of car (Gen 3). The radio info is around page 226. The wiring is a little complicated, but given all the wires are color-coded it should just be a matter of finding and matching up the correct wires. Make sure you understand where the wires from the new radio go to, and that Toyota did not use standard wire colors. An example being red always being just for DC power.
There should be enough original wires going from radio to the amp to change these over to speaker wires. Then jump the wires to the speaker where the old amp used to be. I suggest rather then jumping the negative speaker wires to ground, you match up the speaker wires with the old amp wires running to the radio. If everything works OK great, if you get noise, then start thinking about running shielded wire directly from the radio to the speakers.
After you hook up all the wires, it might be best to check the circuits with an ohm/volt meter just make sure everything is OK before applying power to the radio.
http://oregonstate.edu/~tongt/camry
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