Some years ago I was taking an IPC and FR in a Piper Aztec. A few minutes into the climb, I shut off the aux pumps, one at a time. A few seconds later, one engine quit. I turned the pumps back on and the engine restarted. After leveling off and setting low cruise power, I tried turning off the pumps again, and found that the left engine was the problem. It would run fine with the aux pump on; not at all with it off.
I assumed that the engine-driven fuel pump had failed. I called ATC and said I was returning. On landing rollout, the left engine quit and wouldn’t restart. I foolishly taxied to the FBO on the right engine, a fire truck following uselessly. As I shut down the right engine, the chief mechanic appeared and told me in a loud voice that there was fuel dripping from the left nacelle.