I'm just now getting back to this forum and it seems that I have caused quite a stir.

I read all of the posts last evening and thought about what has been said here. It does make sense to try to match bulb wattage with the device under test and use low wattage when investigating a known faulty circuit. I then thought I would run a few experiments and measure some voltages to try to better understand all this.
First I went back to my known bad mains power supply transformer. This transformer is electrically isolated and disconnected from the amp circuitry. To recap, whenever normal 120V is applied it hums loudly and heats up very quickly and I've only ever tried powering it on for a few seconds at a time. It's bad so I thought a few experiments aren't going to hurt anything.
So I tried using a 40W, 100W, and 250W bulb one at a time to see what happens. In each case, the bulbs turned on as expected and the transformer never made any audible hum and it never seemed to heat up for that matter. I measured somewhere around 35V for what is actually making it to the transformer for the case of the 250W bulb and smaller voltages for the other 2 bulbs.
For US power I would calculate that the fully-heated on resistance of the 250W bulb to be somewhere around 58 ohms. If I am seeing a power drop of 120V to 35V across the bulb then I believe that means we are looking at a current of almost 1.5 amps flowing through the circuit. (All of these are crude numbers but I think they are in the ballpark). So that definitely looks like more power than one would want when investigating a faulty circuit.
The second thing that I tried was then plugging in a good working Peavey TKO solid state bass amp that I happened to have on hand. I believe this amp is rated for a maximum power draw of 200W.
With the 40W bulb plugged in, I measured around 95V being supplied to the amp. With a 100W bulb plugged in, I measured around 108V. With the 250W bulb I was seeing very little voltage drop at all from the original 120V.
So I can see that with an assortment of bulbs this can be used as a "poor man's" variac. It also looks to me that the larger bulbs aren't totally useless either. If you have a piece of equipment and it has been repaired and after applying higher and higher voltages with assorted smaller watt bulbs, wouldn't it still be useful to use a large wattage bulb as your final test where you are supplying as close a value to wall voltage while still having some (although admittedly not great) power protection?