Thanks to Jack Zhai's suggestion, I figured it out.
When the breakpoint is hit, unpause the debugger (shortcut: F5)
Play to the point in the game you want to debug.
Repause the debugger using Break All (shortcut: Ctrl-Alt-Break)
Press F10 a few times; this makes it go a few more steps in the main livewires loop.
In the autos window, there is an entry that contains the a list of the game's objects. Look through it, until you find the one(s) you're looking for. In my case, the list of the objects was self._objects. The object I was looking for was the second, which in other words, was self._objects[1].
The dropdown arrows of the object(s) you're looking for show the object's members. If you want to look at the object's properties in a less cumbersome way, use the Interactive Debugger to assign that object to a variable. That way, you can look at its values through typing objectNameHere.objectValueHere into the interactive debug console.
In my case, I had to type in player = self._objects[1] to get it assigned, then could see the player's x position by then entering player.x into the debug console.
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I know this answer might only work for my specific problem, so if anyone else has a better one, please post it for others' sake.