The stem should get very hard, and there should be no, or very light light green lines radiating from the top of the stem. It's better to pick them more ripe than less ripe. Less ripe tend to be astringent inside and not very palatable.

Mine are tan too, but I don't think they're ripe until the stem turns brown. I'm basically going to wait until the plant dies or just before first frost, whichever comes first.

I don't think that pumpking/winter sqash can get overripe like watermelon, cantilopes...because they have much less water and sugar content.That is why they can be kept for months. I grew up somewhere with very short growing season. Over there, after the vines died the pumpkins were technically ripe, but people used to set pumpkins in the sun, to get real nice orange/red color and sweeten more.
So I don't think pumpkins can get overripe.

FYI - my evil squirrels were starting to take a nibble at the squash, so I went ahead and picked them. Out of curiosity, I cut one of them open. It was a nice golden color, with a large area of "meat" and a smaller than usual seed mass. (Maybe due to picking on the early side.) I cooked it and it was gorgeous and sweet! I pureed it to put in the freezer and the stuff was smooth and lovely! I'm so excited. I am going to store the other one for a while. Since I picked those two, another squash has started to grow. I hope it makes it -- the vines are starting to get powdery mildew.
The whole garden is suffering in the hot weather.
But I got some squash -- woo hoo!
Thanks for all the help!