2006 Toyota Camry radiator issue

First, it appears to me there's shmoo all around the neck. Remember, water only runs downhill. If you're not seeing it spray when it's hot, then there's just about no way for it to be coming out from where you're pointing at. Secondly, look to the easy fix first. You can at least discount it. The cap is by far going to go bad before the radiator itself.

You could test the cooling system with UV dye to get a better picture, but I'm pretty sure it's pretty clear the general area the leak is occuring. You could also do a pressure test on it, which would tell you right away if the radiator is leaking. To introduce pressure, you'd have a separate cap which would allow you to pressurize the system. If you don't find anything, then the leak is coming from the cap. You can also look under the top of the cap, to the outside of the seal. If the shmoo is there as well, it's a pretty good sign. A cap might only leak in one spot (where it's weak), so it may only be there's shmoo on only one side of the cap. Don't discount the cap because of this.

A cap costs about $5-10, while a radiator will cost more in the range of $100. If you end up having to replace the radiator, you'd want to replace the cap anyway, so you're not going to be out any money. It wouldn't be required, however, it's just not a bad idea. New radiator; new cap. Kinda go hand in hand.

As far as fixing the radiator, it's nearly impossible to repair the plastic portions of a radiator. There's just about no way to seal it and get it to hold pressure. You could if it was metal (or at least there's a chance you could), but not with plastic/polymer ones.