Tube emulation, although it looks technically easy in the first place, is not a simple task.
There are so many variations of tube powered devices, each with it's own, distinctive charachteristic:
• Look at the tube version of the German's broacasters workhorse tape machine, the Telefunken M10: a chain of a multitude of tube circuits, all do use a lot of NFB to control their behavior.
Result - not the slightest hint of "that" tube sound you would expect. This is, of course, on purpose, the broadcast sound has to be natural, uncolored, transparent.
• The other extreme: your 20$, underpowered single triode chinese buffer amp of probably questionable design:
All kinds of distortions, limited dynamic range and frequency response:
Seems just exactly what's needed for your purpose, but should this be the model for an emulation?
A lot of these emulations of all kind are already available as plugins.
Sucessfully and detailed emulations of all time classic studio devices —
UAD's LA2A comes into my mind.
UAD builds both, the original hardware still, and their own emulation that uses quite some DSP power.
One may not forget, a tube circuit more then a solid state one, largely depends on it's surroundings, levels etc.
A traditional tube power amplifier interacts, not controls a loudspeaker or headphone.
The sound of the VF14 tube inside the grand-daddy of all tube powered microphones, the famous Neumann U47, is unrivaled even by it's nearest achestor, the EF14 tube.
The reason again is an interaction, with a special power scheme - and the output transformer used.
I went the other way:
Designed and built special purpose tube amplifiers.
E.g. a 1W OTL SE triode headphone amp for the AKG K1000, and a comparable design, a 10W version to drive my Electro Voice Sentry III up to earsplitting levels (what I never, OK, almost never do).
Very low NFB gives a pure triode characteristics, tube as pure as tube can be:
Lot's of harmonics, 2nd order spiced with a bit of 3rd oder only, softly develop over a exceptional wide level range, enriching the sound in a "natural" way.
Coupled with the super precision and cleanliness in the lower level range, typical for OTL- (Output-Transformer-Less-) tubeamps.
These amps have a coincidence with the headphones / speakers driven, not by chance but by design.
Your "tube buffer" likely has such a coinidence too.
My idea is: if you want the real thing you need the real thing, at least it's the shortest shortcut to this destination - and it's fun!