Since I didn't know the difference between bake and broil, I turned my oven to bake and it did a 6 minute preheat as displayed on the control panel. The bake element stayed on continuously and the broil element cycled on and off, just beginning to blow red before cycling off. This was signaled by the clicking in the control panel similar to what I heard on the MIL's oven. Once the oven went into the normal bake mode, the bottom element cycled off, so I'm assuming it has to do this to not overheat. I didn't see the broil element ever come on, or if it did it wasn't long enough to glow red. I heard some clicks but sometimes couldn't tell which element was doing what. I had the lights off in the kitchen in an attempt to see the color of the elements. My MIL's broil element only had power for a matter of seconds, which doesn't seem like enough time to heat up, but maybe that's the way this oven works.
My MIL claims that she can tell if the oven is working right by the way it's cooking, and it's hard to argue with your 92 year old mother-in-law, if you know what I mean.
EDIT: I'll check with her tomorrow, but is it possible that this range has a manual preheat, and when I tested the element, she put it into preheat causing it to stay on? And maybe this time she put it on just bake? Would that have made any difference?
EDIT2: Now that I understand a little more what to look for I'll check the range tomorrow, and I'm wondering if when I installed the element she put the oven on bake and cranked up the temperature. Maybe this caused the broil element to run longer. Yesterday I know the oven was on 350. I found a copy of the manual online and didn't see anything about preheating. Anyway MajorApp, I appreciate your time and advice.