What's known for certain: It's very similar to Conserve MP in some ways and very different in others. The similarity is that equipment only affects the proc rate (base 25%) and not the amount, and the difference is that the amount conserved is always 1 to 20. As you tell from reading this and from your experience, Conserve TP doesn't exactly return buckets of TP.
What's foggier: How Conserve TP does or doesn't stack with Save TP exactly. This is a hard thing to test because it requires time to gain TP, certain buffs on certain jobs, consistency across weaponskills, and some other awful stuff that skips my mind at present.
No one has ever once reported that the two simply stack straight-up, yet this would be very easy to see if a high-end Conserve TP activation that provided 10-20 TP occured in Voidwatch or under the effects of Miser's Roll and only one single occurrence would be needed to prove the possibility. Since that one occurrence has yet to be reported, it seems unlikely they stack in a straight-forward manner if at all.
If they do "stack", it seems more likely that the higher amount between the two simply wins. Given that most sources of Save TP are over 20 at present, this would have the same end effect as the two traits not stacking at all.
It's very possible more people were complaining about Hagakure being adjusted than I originally thought. The many one-sentence-long "They're favoring Samurai because SE employees also enjoy rice balls! I HAVE RAGE!" posts read about the same while I was skimming the topic for meatier posts so I just figured they were from the same handful of people.