If I wanted to install one of these mini flexible strips in my glove box, where would be the best wire to tap into for power?

 

Just so long as it's fused, any wire with power on it.

 

Those don't hold up well to heat. I installed a 48" strip in my boat for cabin accent lighting and the heat during the summer turned it brittle. Ironically, you also need to apply heat to get it to unwind and stay straight during installation.

 

That would depend very heavily on the exact part you get. Surely by now someone has come up with a temperature-rated LED strip for automotive use that will stand up to summer heat.

 

But then they will always stay on. You could probably hook it up to some kind of switch that turns them on when you open the glovebox, and turns off when you close it.

 

True, but it's in the glove box. If you want to get fancy, find a lever- or plunger-actuated switch and have the door actuate it when you open the glove box.