I was able to recently identify a non uniform tire on my car by using the "pen" method-- jacking up the car and resting a pen on something. Having the tip of the pen touch a part of the tire, and then spin the tire. See if a bump comes along and moves it. Car was due for new tires anyway-- which it got.

Since you don't have time to wrench these days, the pen test is a good one that can quickly rule out the tires.

The brakes pulsing when you apply pressure says brakes issue to me. I'm assuming you can feel the pulsing through the brake pedal, right?

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1982 240D 4spd, 327,000mi