I probably should have done a little better job of recording the components and even, as suggested, try to draft a schematic. The rocker switch is soldered to the board and I had to re-solder them to put it all back. I was a little reluctant to go back in there and take the camera out...then I remembered that I am the one who asked about it - and a phone camera is always handy.
The T92 is a 78L12 regulator. Not surprising that it is a regulator but it is a 9V relay so I am surprised that it is not a 78L09.
You can see the size of the AC cap and the value 155K I am reading as 15uF (15 x 1000000 pf), 10%, 250V

There is nothing on the other side of the circuit board. The grey block is a 224 cap (metal film?).
The shunt resistor R2 is marked on the circuit board as .08 2 watt - are you sure that isn't going to act like a fuse - although at 2W that wouldn't make sense, I just don't get why the wire and not a "normal" component? Edit: but a wire of specified diameter and length might be easier to supply than a 0.08 ohm, 2W resister...so n/m.

I guess that I am curious because I just don't see these on cheap floor lamps. I am wondering...Around the time of purchase, I remember that there was a hubub about halogen lamps and fire. By limiting the wattage, you could stop folks from using 200 W halogen bulbs in there - that kind of thing. I just don't know, but that was the direction I was thinking about.