The most consistent sonic tube signature is not the sluggish droopy ill defined sound of the golden era of "hi fi"!
Instead I am convinced it is a much more pronounced 3D soundstage. That is if you are talking of the currently produced tube amps. The degree of upper end sparkle and controlled bass, is very variable. That is clearly audible however there is in addition a very important psycho-acoutical sound.
It is referred to as a distortion, but you can't pick it out it is sort of invisible, if you will. I think is 2nd order distortion. Again I can not describe it but it is there and most people really like it. I can say what it is not.It is NOT poorly defined, fuzzy, rolled off, sound or anything of the sort. It is a highly desirable harmonic phenomena.
If you want to hear what I think people refer to as tubey, then you might try to find a tube amp from the "golden era of Hi Fi" i.e. the 50s until the mid 60s". That would be the extreme of the misapprehension of what a typical modern tube amp sound. It is by all means coming from a tubed amp you are thinking of what you heard 40+ years ago. And for all of you who think I don't know that current tube amps vary widely from directley heated triodes to push pull to SETs and they all sound different you are incorrect. However if you have the experience of listening to a current tube amp of any stripe and say that the usual perception/recollection of tubey, then surely you jest.
I happen to enjoy that Hi Fi sound when feeling nostolgic, which is only occcasionally. If you really want to hear the old tubey sound IMHO, Don't forget you will probably hear it best with the same era speakers. For some odd reason I find the source doesn't seem to have the impact it does on modern systems, but clearly a "record player" is appropriate.
Most of these amps are integrated but if component the pre will already have a "phono" stage input, MM BTW. The only other choices were a tuner and reel to reel for the truly insane. I attribute my ability using curse to the Reel to Reel we owned. My father would become increasing frustrated until his rather expansive cursing vocabulary spewed forth. I recall it was about a 50 - 50 chance that it would get tangled up, off track or some other other calamity would happen.
Or I could have simply said just go out and listen to a !@#%%^&* highly regarded, modern tube amp and you will hear what a tube amp sounds like..