I just got a Lincoln Quick Weld (110 VAC, flux wire only) welder for my son's '70 VW bug project. It doenst have provisions for gas, but I can hear that same kinda relay click when you pull the trigger. Im assuming relay control of the motor on/off function is standard on this type of equipment.
(which leads me to think you have a shorted/ stuck relay contact- if the contacts are stuck you might still see the level move, and it would still click, but the contacts might never open)
BTW, be cautious working on a wire welder - when the trigger is pulled the whole spool of wire is electrically live to ground!
