What are some (bi-grid)tetrode tubes with negative resistance?
Checkout the 12k5 data sheet here

What you are looking for is this I believe: -



Test/picture taken from here

And as far as I can tell the 12k5 doesn't exhibit this characteristic but it may be documented somewhere else. However it is a low voltage tube/valve so I have my doubts.

Maybe try some pentodes like this: -