This brings back memories. Again, my dad didn't teach me through verbal instruction all that much, but like you I picked some things up through other means.
He DID teach me to change the oil filters and oil in a car, along with his story of driving a screw driver THRU a filter because the damn thing wouldn't spin off (he was turning it the wrong way).
But the biggest indirect lesson I learned was from him swapping out ceiling fans in place of ceiling lights. Growing up in Gainesville with the summer heat, he (and mom?) decided we should have ceiling fans instead of just lights in our rooms. This involved dealing with wiring and manhandling the thing into place (nobody offered to help him). My takeaway from him doing that was if that idiot could do THAT, I most certainly could. That in turn led me to believe there was little I couldn't do.
With that lesson, I learned myself how to fix running toilets (change out the inner works in the tank, done perhaps a dozen times), changed out entire toilets (3 times now and counting), changed out a dozen locks (and have been making my kids to this in their early teens), etc. Perhaps another reason this dad gets all the sht jobs around the house when things break. Now, I'm no carpenter or electrician or plumber, but I will damn sure give things my best attempt (or two) before calling in a professional (admittedly, has happened many times). This 'I can do anything, just have to figure it out' dovetailed perfectly with growing up to be an engineer, and has been applied to many various things throughout my life. I always look back and recall 'if that idiot can do it, I certainly can'.