First, Is this a UL 142 tank?
The proper way to fix this, and I am guessing it is a bottom connection, is to remove the nozzle completely and install a new nozzle. This will involve removing a portion of the outer shell where you can get access to the back side of the nozzle.
This will need to be roughly 12 inches square. The smaller the better and if the nozzle is close to the "knuckle" you will need to be aware of weld spacing. However if this is a UL 142 tank, maintaining weld spacing is irrelevant as the tank is no longer a UL142 Standard Tank. More on this later.
Cut out the entire nipple and replace with new Sch 80 pipe.Weld the inside, SMAW with E6010 two pass minimum. Let it cool.
Spray diesel on the outside and let it sit for a minimum of 8 hours, overnight would be better.
Visually inspect the weld and if there is no indication(s) clean the diesel off and weld the outside.
If this is a horizontal tank pressure up the tank to 3 PSI minimum to 5 PSI maximum. Have a 10 PSI gauge with quarter pound increments. If it is a hot day, watch the pressure closely. Have a 5.5 PSI pressure relief on the tank. If this is a vertical tank, rather uncommon for double wall but, have the pressure 1.5 minimum PSI with 3 PSI max and pressure relief at 3 PSI max.
When the tank is at pressure, apply a soap solution to the weld. If there are no indications release the pressure.
Weld a lap patch over the area you cut out for access to the nozzle . If the toe of the patch is within 3 inches of the tank "knuckle" you will have to replace the "knuckle". After welding the lap patch, vacuum test at 7-10 inches vacuum and hold for 24 hours with loss of no more than 2" in 24 hours allowed.
The deformation you see when you pull a vacuum is normal and necessary. Or stuff breaks!
Now the bad news for the owner. While this repair will make the tank capable of holding liquid, it can no longer be considered a UL 142 tank. This means the owner cannot legally sell the tank as a UL 142 tank because of the repairs.
This is no skin off you, as you are only doing what the customer wants. But when the required inspection of the tank is done and the inspector sees the repairs, the owner has no documentation for proper welding procedures or qualification of the welder.
STI has SP 031 Standard for Repair of Shop Fabricated Aboveground Tanks for the Storage of Flammable and Combustible Liquids spells out the extent, requirements and limitations of repairing these tanks and R912 Installation Instructions for Shop Fabricated Stationary Aboveground Storage Tanks for Flammable, Combustible Liquids gives the testing and pressure limits for pneumatically testing these types of tanks.