[Radioroslyn]

I missed that part.
Well.....just use an ohmmeter and see if the primary has continuity to the case.

May work but may not tell the whole story. The primary may need to have the HV present to show the short like if it was arcing.

I think trying to repair the old transformer is a waste of time. I have heard of soaking transformers in polyurethane to try to re insulate them but it depends where to short is. And there is always the possibility of the pri going open at some point too. I think it's just better to replace.