On Sep 5, 6:45*pm, Gordon Shumway wrote:

It could be the switch, the connection(s) at the switch, the wires
from the switch to the fixture, the connection(s) at the fixture, the
fixture itself or the bulb.

Doesn't anyone have any troubleshooting skills anymore?

Well, I was hoping for a technical description of the problem. If I
just replaced the broken part, I wouldn't understand what the root
cause was.

Anyway, thanks to everyone for your ideas -- the problem was the
switch. Specifically, a worn out contact. The reason the bulb
flashed before turning off is because the impact of flipping the
switch was enough to cause a temporary contact inside the switch.
Slowly flipping the switch would do nothing, and pushing really hard
on the switch causes it to stay on (but then turn off when I stop
pushing).