Dan, without knowing exactly what you have there I would caution you against fiddling with the bits inside. The spark gap contacts on
my tig welder are connected to some very large capacitors that retain a tremendous amount of voltage. I was warned by a factory service technician to discharge those capacitors (safely) with a large resistor before attempting to adjust the gaps if needed. Those things can kill.
IF that is what you have there. I didn't think inverter welders used spark gaps, but there is likely a 99% chance I could be wrong about that.
With not having any idea of what machine you have there, all I (we) can do is speculate as to what those parts actually are. Knowing what company made it, and what kind of specs it has certainly helps. I am assuming it is a DC only machine? And you said it does (did) have HF start capability?
Finding a schematic for the welder is pretty much crucial for most folks who aren't in the welder repair business.
Taking it to a shop would be the safest thing to do, although likely to be expensive depending on the honesty of the worker bees. It could cost more than the price of a new welder.