Thank you all for the replies.
I'm using electrical solder. Lead-free 96/4 silver solder (Radio Shack brand).
I'm
not using plumbers acid flux. Thank you for the long write up about it though.
I'm using this
Tip cleaner. Maybe that's the culprit? It doesn't say what it's made of.
I believe the iron tips were chrome plated. They were shiny before use.
No variable control, this is a cheap ($10 USD) iron that came with 3 tips from a big department store.
I was wiping the tip off between uses on a natural cellulose sponge. Damp, not wet. I see two conflicting answers about leaving solder on the tip vs wiping it off. Perhaps I'll try leaving it on.