Macbook Pro Mid 2012 Black Screen and No Picture On External Monitor. GPU problem

I would put a lot of weight in a technician that sees many macs as they really don't have any reason to mislead you. You can also get a second opinion if you don't feel the one you got the first quote listened to your concerns or explained how he arrived at that guess.

Do make sure you look carefully - when the backlight goes out on a LCD - there is so little light coming through it is hard to tell if the panel is drawing fine and the light is missing or the panel isn't being driven.

Without opening the mac and trying to replace things (and especially when it's intermittent) it's hard to know for sure what one piece is failing. If you ask a tech to put percentage chance you will find most situations have multiple causes, but one is much more likely given experience and symptoms.

The next time it goes out - you can use a flashlight to narrow down if the panel itself is not getting signal or it's just the backlight by looking for the menu and other graphics on the screen getting drawn.

Since people are still commenting on this, I will post what happened as my answer: I took the MBP to a different store where they concluded that it was a faulty HDD cable since I had installed the SSD myself and they assumed it got some kind of shock for me not wearing an ESD bracelet. (Although as far as I can remember, the friend of mine who installed the SSD for me did indeed wear the bracelet, however I probably didn't use it when I installed RAM 1,5 years ago)

It seemed to work fine for a while but after that, the glitches started to reappear, and it became so bad that the MBP couldn't boot into OS X or Windows (stuck on grey screen with glitchy stripes).

Once again, I took it to the shop, they concluded that it was a faulty logic board, which would cost me a fortune to replace. However, thanks to EU consumer laws, I have the right of up to 3 years warranty if I could prove that it's the manufacturer's fault. So they let me fill in a form and send it in along with my receipt. By the beginning of July, Apple finally approved to replace the logic board for free. For now, the MBP is working properly again.