Excellent advice. If I have an issue like that, I have a sympathetic tire shop remove the wheel and tire, then I roll the wheel across a flat section of shop floor while I track it. You can spot all sorts of issues doing that if the wheel is out of round or not balanced.
Another thing to check for when the tire is off the wheel is small rust spots. The few I had were on a painted wheel. And the paint on the inside still looked really good. It just had several tiny rust holes. These rust spots can sometimes work their way all the way through the steel, and you'll get up one cold morning and find you have a flat, but you fill it up and run the rig all day, and it holds air. Most shops wouldn't even think of looking for rust spots on the wheel, they concentrate on the tire so you end up stopping at shop after shop until you eventually find a thorough tire tech who's run into the problem before. Once the tire warmed up, steel expands so I'd get to a shop and the leaks had sealed themselves.
The shop that finally found the leaks couldn't find a 19.5" steel wheel in town so I took Eternabond tape and covered all the holes or potential holes, and drove it like that for several years afterwards with no leaking.