"Improved vacuum tube models for SPICE simulations" https://normankoren.com/Audio/Tubemodspice_article.html
The intractability of the Triode is part of the reason why the Pentode exists. And, you will note, the Pentode curves in certain modes looks a lot like your bog standard MOSFET.
This also discusses how the "constants" ... well, aren't. https://www.john-a-harper.com/tubes201/
With that said, a N type JFET is not a bad start. The main rules of thumb work: The grid draws negligible current. The tube will pass enough current from plate to cathode, to maintain a roughly constant cathode voltage above the grid.
But tubes aren't current amplifiers, they're voltage amplifiers, like FETs.
You can look at the "characteristics curves" of tubes (plate curves and transconductance curves), which tell the story of current against plate-to-cathode voltages for fixed grid voltages.
Gives overview equations for MOSFET device simulations which are probably sufficient for most purposes in Section 3.5, and COMPLETE mathematical descriptions of the SPICE MOSFET implementation in Appendix A.3. Not for the weak.