You can do it but they intentionally make it difficult. It is near the motion sensor and they have a clear cover so the light bleeds through the side if you just tape it. The purpose if so you know when video is taken. I actually like it because I want to know when it is recording so it doesn't record an embarrassing video by accident. Imagine walking past naked. Then, later you show someone how it works, oops!
Many other features that I thought I would not like, I now prefer such as the LED light instead of infrared. Color vision at night is better than black and white and since it is a "security" camera, don't you want to scare away an intruder instead of just record?
Also, other "cons" reported in the one Amazon review such as "motion sensing zone" are not practical with a battery operated camera. A separate motion sensor takes almost no battery. They could add some of these features in the future for powered situations, but just not practical for battery operation which is their primary market.
At the risk of sounding like a Blink fan boy, I would recommend getting at least a pair (prefer five set) and trying them out. For the price and ease of use, it is worth the "risk", in my opinion.