The transistor's terminals aren't labelled in the drawing in post #14, which represents the transistor as a rectangle with 3 leads.
I used a proper transistor symbol in my version and I assumed that it should be a common emitter configuration.
Yes, I meant to say collector. Unfortunately this forum doesn't allow you to edit posts or I would correct that.
The transistor I used is unmarked so I couldn't look up which lead is which. I'm only sure that it is NPN and which is the base because of testing with the ohmmeter.
45 years ago when I was fresh out of college (Electronics & Acoustics) I might have thought of measuring the current with it connected each way to determine which is base and which collector. Now that you have refreshed my memory I'll try to remember to do that the next time (I have a feeling that re-learning some of this stuff is going to be harder than learning it the first time).
Re the 200Ω base resistor, I'm not even sure if that is necessary because the HC-SR501 has a 1K resistor in series with the output but resistors aren't expensive and in this case it worked out that the resistor's stiff leads support the transistor.
A total of 1.2KΩ in series with the base would mean that the current would only be 2.25 mA so any saving would be truly minimal, especially since I am powering it from an AC adapter.
BTW: I have installed motion sensor LED light bulbs in all of the places where people don't normally stand still very long (hallways, closets &c), including at the bottom of the stairs just outside of the door to the shop, which you can see it through the doorway in the pic of my homemade PIR LED light installed. When you enter the shop there's a sort of alcove and a couple of steps to the light switch where the room becomes full width. This means that the light outside the door is always on when you enter the shop so finding the switch isn't a problem but leaving the shop involved turning off the light, finding the door in the dark and going past it far enough to activate the light outside without tripping on something.
With my homemade PIR LED light I can now see where I am going
The screw terminals on the side of the box are for adding more of the 6 LED lights if I decide to later on but I'm going to try it for a while with just the one first.