Hi sls25, Thanks for the photos.
I believe you are looking at the tank covers. Mine is metal, but maybe in 05 Airstream made them out of plastic. The purpose of the tank cover is to hold the tanks in position, and to hold heat for the tanks so they don't freeze in cold weather camping.
So seeing water coming out of these holes does not necessarily mean your tank is leaking. Heck, with the rains we have had lately, it could just be rain water. Airstream belly pans are known for getting water in them. This explains why you can put your finger over the hole, and when you release it you get a stream of water. It is pooling in the pan.
So run a test. First, disconnect city water and turn off your water pump. Then drain your fresh water tank and let the trailer sit for a few days until there is no water dripping on the ground. Check it again after a rain storm. If you see water, then you know it is rain water.
Next fill the fresh water tank through the fill port. Let her sit and see if you are getting any water dripping. If no, then you don't likely have a hole in your tank.
Lastly, now hook up city water to your trailer and pressurize it. Don't run any more water in any faucet in the trailer except to get the air out of the lines. Let her sit a day or too. If you see dripping, you know you have a leak in your fresh water plumbing, likely somewhere over the fresh water tank. If still no water, then disconnect city water and pressurize your system with the 12v
pump. Maybe there is a leak associated with the little bit of plumbing distinct with the 12v
See what you can figure out concerning this leak.