I was out to do some shopping but took a random detour, following my feet. The detour just happened to take me to a suitable road junction, at exactly the right time. By rights, I shouldn't have been there to take the picture.
But "lucky catches" aren't just about accidentally being in the right place at the right time by nothing but dumb good luck, or about preserving a certain random element in your approach (although that certainly helps). If you want to be able to catch something that other people miss, you have to expect to spend at least some of your time in places where they aren't, and looking at things that don't always seem to be immediately necessary to the job in hand. You also have to be prepared for the possibility of success (I try to keep a camera with me, and it had just enough juice left in the batteries to fire off a few shots for the critical sixty or seventy seconds), you have to be able to recognise the preliminary signs of something interesting (I saw a faint 'bow forming, realised what was coming, and was able to fish the camera out and find something to shield it from the rain, in time) and you also have to be prepared to look stupid (standing in the rain with a plastic folder over your camera, taking photos of the sky, at an angle where most of the people who can see you have no idea what you're doing).
But the main thing is to have your eyes open. If you're absolutely sure that nothing interesting is going to happen, then on the occasions when it does happen, you're liable to miss it.
The same thing goes for theoretical physics. If you want to catch things that have eluded other people (whether it's math, or theory, or experimental research), you don't always have to be so much smarter than everyone else, or to have better equipment. Sometimes it's enough just to be prepared for the possibility of being surprised. If you're too rigid about what you're trying to find, you miss out. In my case, I was popping out for a plank of wood for some shelving, and I came back with a plank of wood and a bloggable photograph of a rainbow. If I'd been more singleminded in my shopping, I'd have only come back with the bit of wood.