NES screen blinking without a game

I just found my Uncle's NES in my Grandma's basement and he said I could have it. When I took it home, plugged it in, and turned on the red light blinked (I understand this is normal), but also the TV screen flashes light green. A game is not inserted, although when a game is inserted it does the same thing, but I do know this is normal and I need to replace the 72 Pin Adaptor. I was just wondering if it would do this with no cartridge inserted? Should it still blink? Thanks!

The constant cycle of blinking is a sign that you're having an issue with the 10NES lockout chip in the NES. This chip has to be able to connect to a similar chip in the cartridge or the NES resets itself every second. This causes the blinking of the little light and on the video out.

It's normal to get this behavior with no cartridge in, but if it's happening when a cartridge is inserted, it can indicate some problem between the cartridge and the NES.

This could be the result of a dirty or worn 72-pin connector, or it could be an issue of communication between the console's 10NES and the cartridge's sister chip.

You can disable the lockout chip in the NES by opening the console up and cutting pin 4 of the chip. I covered this in this answer and referred to this wiki for information on spotting the chip and the particular pin that needs to be cut.

That wiki article also discusses cleaning or replacing the 72-pin connector, which is usually accomplished via a cleaning kit of some type. The ones Nintendo (used to) make are pretty good if you can get one. If you don't mind taking it apart, using alcohol and cotton swabs will clean most surface grime, and you can use a very soft art eraser to rub off any significantly caked on grime.