Is the trolley problem actually a good way to determine Fe/Ti and Fi/Te?
Not saying you will always pick the same choice no matter what but you how you actually come to your decision might be a good way to determine it.
For example I feel like most INTPs would pull the lever because Ti (5 is greater than 1) and Fe (how will the community recover from the loss of 5 people vs 1). And pulling the lever doesn't really redefine who I am as long as you had a good reason (Fi demon).
However when Fi is involved, that skews the probability towards not pulling it as the choice is no longer obvious. If you do pull it you become a murderer in your eyes and that realisation is more disturbing to an Fi user who might struggle with their new identity. Even if they're a Te user, the weaker Fi might still eat at them in the back of their mind and thus still create friction.
For me it's a no brainer and I was always baffled by some people would say they would not pull the lever to save more lives.
Edit: To keep it simple and avoid confusion, assume you have time think it over, you don't actually know who you are saving, why they are tied to the track or any other external information. You simply have to choose between 1 or 5 lives by pulling the lever or not.