Thanks for the link, wblock. My handle seems to have been repaired at the strain reliefs, but the seller confirmed me it was working before shipping. I'm willing to believe him, but he was selling more than one so tests might have been done with another iron.
I took resistance measurements of the tip (results match spec) and at the connector and only found 3 pairs of pins out of 15 possibilities that where in the 3R range.
Both of my tips are new and exhibit the same behaviour, so I think I can rule them out. Taking temperature measurements with or without pressure or wiggling don't change the results.
Looking at your experiences, I think I'll buy a new handle and see from there.