Why did my light string turn off after a short while with GU24 to E26 to socket outlet adapters?
My first guess would be that your existing (presumably outdoor fixture) socket was connected to a "dusk to dawn" photocell (light sensor) somewhere, with a 2 minute delay (not uncommon) to automatically turn your outdoor fixture on and noght and off when the sun comes up. So when you turn it on, the light from your string lights is enough to make the sensor think it is dawn and it turns off. Usually if the existing outdoor fixture had a flood lamp in it, the light from it was directed away from the sensor so that didn't happen, but the string lights are spreading light in all directions, so now the sensor sees it and reacts. 

Look for a photocell or sensor somewhere and if you find one, cover it with something dark, like electrician's tape. Sometimes, like in the example below, they provide a sliding metal cover to use for this purpose.

The photocell may not be a separate device like this however, it might be built into the fixture itself. But the "cell" might look like that round area with the squiggly lines in it. It also might look like the gray area on the top of this example: