Actually my Ti has always been very strong. (My Dad is an INTP and I think that is why.) But Ti never gave me a solid foundation. It's always been just a way to analyse ideas. It's efficient yes, but does not give me any sense of identity.
A few years ago I significantly developed my Fi though. Now Fi is something that can really give a person a strong core. I get my identity much more from Fi than from Ti.
I'd speculate that the reason why you did not get a strong identity from Ti because you have not learned to use it in a way to build identity. Most INTPs manage to accomplish this. This has been featured most dramatically in history in character of Socrates, Aristotle, Spinoza and recently Einstein.
That is because Ti is a function of introverted judgment, it seeks a higher purpose in nearly everything it encounters. Or as Leanor Thompson put it, an internal purpose, one that transcends the convention.
To say that Ti can be used only for analyzing is tantamount to saying that Fi is used only for empathizing. No doubt this is how F is used externally, hence the reason why EFJs tend to lack a sound inner identity, but Fi goes beyond that. To ignore this means to ignore the introverted judgment aspect of Fi and Ti.
I think that the reason why you were unable to derive a sense of inner identity from Ti is because you have externalized it. As you said, you used it only for analyzing.
I also speculate that it is not really Fi that is giving you a sense of higher purpose. It is Fe that you've developed and its working through your Ti. Ti first sent you inwards searching for the purpose and Fe backed it up with emotional energy and hence made it look like Fi.
I am not saying you dont have Fi at all, but it works from behind Fe, and therefore necessarily less influential.
Here is the order that functions tend to grow in.
Ne(0-10)
Ti(10-20) reinforce Ne
Ni
Te(the further down the list we go, the greater the gaps will be)
Fe(20-30) reinforce Ti
Fi
Si (30-40) reinforce Fe
Se
40-50, Reinforce Si, the second function of the same kind grows simultaneously as the prominent, though at a significantly slower rate.