This is common with Toyota's...it is not a Camry or solara or tercel issue, it IS simply a relay issue. Sometimes a simple reseat will fix it but if not, go to the local wrecker and strip 4 or 5 models that are the same as yours. After you have done this swap from one to another til the issue is resolved.
Also the relay box under the hood comes right out with two bolts and is undone with only unclipping the harness (takes about 1 min to get them all) they are coated in white protectant.
Any dealer that takes an interest can find this "known issue" in the dealer data-tech system provided to their parts and service dept by Toyota.
Good Luck and feel free to ask anymore ?'s you have.
Sidler
http://www.offroadaction.8k.com/
http://community.webshots.com/user/offroadaction