I agree with Herr Rolf, based on the references posted by Fredsmythson and dr_nybble.

You want the hot line from the power cord to connect to the fused line that runs to the power switch. In the snippet of the Doodle Bug schematic that Rolf has posted, this is denoted as a yellow wire. PLEASE VERIFY THAT THE YELLOW WIRE INDEED GOES TO THE LINE FUSE!. If it does, then the hot wire connects to the yellow wire. The power cord hot wire will be the line that comes from the small-prong opening of the receptacle. In the US, the small prong opening is always on the right side of the outlet. With the power cord not plugged in, you can verify this with a multi-meter set for continuity check or for resistance check.

What is confusing, is that Rolf's schematic shows the neutral wire as being black, where your machine seems to have a brown wire emerging from the wiring bundle??? Not sure what to make of that difference.

OK, Please ignore my advice from the previous post.
The pin repair guides indeed say: The "hot" (black or smooth wire or narrow prong) should connect to the line going to the power switch. According to the schematic snippet, that would be the yellow wire.

However, I have a Williams EM where the left-side prong is connected to the yellow wire. Until I figure out which should be which, ignore my post.