Welcome to JustAnswer.com! My name is DriveFast71(Ron) and I will do my best to answer all of your questions completely and accurately.
Did they happen to give you a "p-code" that went with this description?
Ok. To correctly diagnose the actual problem, we'll need a "p-code". I guarentee that the mechanic has already gotten the p-code, as that's where we ALL start. These p-codes are the "diagnostic trouble codes" and tell you, with a degree of certanty, which part/sensor in which system has the fault. For me to best help you, we'll need that p-code. You can have these p-codes read for FREE (except in Cali) at any local "big chain" parts store, like AutoZone. Once you have these p-codes, we can more accurately and efficiently diagnose the problem, and then begin the repair process.
ok. P0455 is "EVAP System Large Leak Detected". There are actually quite a few different things that can set this code (see chart below). Very commonly, however, this is a loose, missing or faulty Fuel Cap (even putting fuel in while the engine is running will set this code). Inspect the o-ring on the underside of the fuel cap for any cracks or chips. Inspect the fuel filler neck for any dirt or debris that would keep the cap from sealing. If the cap checks ok, and you are sure it is good (those fuel caps they sell at AutoZone will NOT seal the system, so if the cap needs replacing, it needs to be as close to Toyota original as possible!) then you will next need to inspect the vacuum lines around the fuel tank and EVAP canister area. Look for any lines that have cracks, holes or loose/missing connections and inspect the canister itself for damage. If the visual inspection checks ok, the canister purge VSV will need to be tested for proper operation. If all this checks out, then the next best way to diagnose this, is to have the EVAP system "smoked". This is where a machine forces smoke through the system, and the "large leak" will reveal itself.
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I would. And find a different shop to give you a 2nd opinion! Why spend $1300 when you might only need a $20 fuel cap!