Blinkers ( both sides ) blink a couple times and stop on 2001 VW New Beetle

SOURCE: 1973 vw beetle sedan--turn signal

i beleve the flasher on this cars, i suppesed to have a ground cable
most of times it is brown color, try to locate the flasher and make sure you have the ground and also the ignition switch power going to the turn signals flasher

SOURCE: 1999 vw beetle 2.0 not turbo. signal lights not blinking

You are talking about the turn signal flasher unit correct?

This is not where or what you would expect.
It's all contained in the 4 way flasher switch located on the same panel that hold your climate controls.
They engineers at VW put the entire flasher control unit on the back of the switch for the emergency flashers.

SOURCE: 98 VW Beetle Turn Signals

Hi, Sounds like bad turn signal flasher relay.

SOURCE: On my 2001 VW Beetle, what causes the blinkers to

POSSIBLY BURNT OUT OR INCORRECT BULB
COULD BE EMER FLASHER SWITCH IN DASH WHICH HAS T/S FLASHER BUILT IN
LIGHTER COULD BE FUSE OR SHORTED SOCKET

SOURCE: 2006 vw jettA 2.5....trouble starting

I had to take my car back to the dealership twice. First, they replaced the ignition switch. 3 days later, my car wouldn't start again. So I took it back and they called VW - VW said to replace the steering column module. I asked my dealer why they didn't replace the steering colum module first - they said that even if they had replaced that first, the old ignition switch would have shorted out the steering column module. Whatever.
$600 later my car has been fine for about 3 weeks now. If it happens again I will keep you posted.
Good luck!