Bigmal, as Karl said, that light should flash when key taken out of ignition, mine does, as stated in Toyota handbook.
The button you are pressing up by the interior light, is not a reset button. It's for turning off the motion sensor intruder alarm, if you leave kids or dogs in there. To do that its not just a motion of pushing the button, there is a short sequence to follow. Its only functional until you next enter/turn on the ignition. To operate that function again, you have to go through the procedure again, so only temporary for as long, and when you want it.
If you dont want that option, leave it alone. From what you describe, your system is normal, unless as Karl asked, your alarm is going off, when locked and armed with remote.
I don't think your glove box light is anything to worry about, mine doesent work either., bulb gone. haha