Where is the pickaxe?

Look for a workbench

In the two runs linked below, the pickaxe lies on a workbench: a low bench with a pegboard behind it and blue storage bins on its shelves. In one run that bench stands in a room lined with blue-green metal cabinets, a few seconds from the start. In another it is a bench under a sheet-metal overhang near the rails, about a minute in.

So it is not always on the same bench. How many benches it can use is not settled: one player who has beaten the Mines guesses three, in their own words “There are three spots I believe that they appear here on the map.”

How you know you have it

If Thomas catches you while you carry it

According to that same player, dying does not lose the pickaxe: “when you die, it will stay there and you have to repick it up.” They also report coming back at the start rather than near the gate they had opened: “When you die, you're spawning way back over here rather than you spawn in the area that you open.” Treat both as one player’s report. The first would match the school, where whatever you carry drops where you fell.

What the game says after that

Once the pickaxe is in your hands, every step of the Mines chain announces itself at the bottom of the screen. These are the lines from the run in the video above; the name in the lighter line is whoever picked the lighter up.