Hello I will help you with your question,
Is your Camry an automatic or standard shift?
The reverse lights are powered from the gauge fuse in the instrument panel junction block (left column second down) which is behind the left side of the dash
It is not lokely that this fuse is blown but check first then let me know if you have a testlight to check for power. If you don't have a light it will be necessary to find the source of the problem. You can buy one for about $5 at big box and autopart stores
Let me know what you find