The more you fly the more mechanical empathy you will build. But yes, some of my students just have it from the word go and some take a long time. The most impressive was a 17 year old girl who had not yet started to learn to drive (nothing to un-learn).
But flying is much more than mechanical empathy of course and I've flown with folk who are great at handling the machine but are terrible pilots with no situational awareness and a bad attitude to safe airmanship.
Knowing that you would like to develop better handling skills, as jetsetter does, is a very good start. We are all learning, all the time. I'd also endorse Mary's glider suggestion - in fact I think all power pilots should spend a few hours in a glider.