To reply to myself (haha)... Okay so LIE-Ni Harmonizing types can resemble SLI's (their supervisors). I am aware not everyone agrees with DCNH theory but THIS is a real thing. I'll come out and say that I get this knowledge partially from an epiphany I have had about my dad.
A while back I asked people to VI my dad. Sol was sure he was ISTj or ESTp, but IR and just knowing him really ruled that out. I had settled on an introverted sort of ESTj typing but Sol was right IN THAT ESTj(Si) never quite fit..... After studying LIE-Ni's I suddenly realized my dad not only looked like one (as a younger person especially) but fit the criteria. And he too appears to be quiet and mysterious in some ways. When I read that Harmonizing types can resemble their supervisors it all clicked.
Anyway, I VI my dad the same way as your dad @aster: LIE-Ni. Is he a Harmonizing type? Very interesting case.