My UL 142 is a 2002 edition and there is nothing about welding requirements in the standard. However, if you are a UL 142 manufacturer then your welding procedures and welding qualifications would have to be approved by UL and I would guess these would need to be approved by UL before you can put their monogram on them.
If you are repairing a UL 142 then it falls under STI SP031
Steel Tank Institute SP 031 Section 5.2 WELDING
5.2.1 Welding procedure specifications shall be qualified in accordance with the original
construction standard, if known, or Section IX of the ASME Code, AWS D1.1, or D1.6