I found a piece of heavy metal wire laying around and it is exactly the width to support the sliding lid on my tenner. Quite stiff. I think it was from a cooling rack. Cut it to the right length and it slides very nicely now, without having to use a finger to hitch it up.
I had been using pieces of wire coat hangers but had to give that up because they start to rust after a week or two so frequently needed replacing and I ran out of coat hangers I was willing to cut up.
Problem is I'm not sure what this metal is.
The end I cut is lighter gray inside, looks like it could be lead? It is above the rim so not under the surface, but I suppose condensation dripping back down could leech something out of it into the water. Maybe I could seal the end of it with silicone. But if the main part of the wire rusts like the coat hangers did, it's pointless to keep anyway.