Just in front of the distributor cap you will see two coolant temperature sensors. The black one is for the dash gauge, the blue one is for the E.C.U..
Take the plug off the BLUE one and measure the sensor's resistance.
It should read between 2k.ohms and 3 k.ohms when cold (20 deg.C.) and 280 ohms and 370 ohms at normal running temp. (80 deg. C.).
Dont run the car with the plug removed.
A faulty blue C.T.S. causes a lot of starting and running problems on the Polo, but they cost less than £10 from V.W. and are easy to fit yourself.
As Hilts says, next time the car fails to start check for a spark. Carry a spare spark plug to test with and a pair of insulated pliers or , preferably, a timing light or H.T. tester.
If there's no spark get the multi-meter out again and check the ignition coil.
The primary winding resistance ( between the nuts marked 1 and 15 on top of the coil) should be between 0.5 ohms and 1.5 ohms.
Pull the H.T. lead from the coil and measure the resistance between the connector in the coil and either of the nuts 1 or 15. It should be between 3k.ohm and 4k.ohm.
This is not a definitive test as the coil should also be checked under load, but the test would cost as much as a coil.
A new coil costs £20/£30 and is easy to fit
The hall effect sensor Hilts mentions will also cause loss of spark if it fails and yours does seem to have the same symptoms mine had. It seems when the car is stopped the heat rises and everything in the distributor gets baked.When mine started to fail it rapidly got worse.
I dont think there's any easy way to test the hall sensor
Apparently on some dizzies the hall sensor itself can be replaced but on mine ( a '94 Mk.3, 1043 c.c. AAU engine which I'm fairly sure was identical to your '93 model) the entire dizzy had to be replaced.Again an easy job to do but a bit more expensive.
Mine cost £92 'service exchange' four years ago from a V.W. dealership (the motor factors were marginally cheaper but didn't have any in stock and I was fed up going out in the car and coming home on the bus!!) and came complete with rotor arm and the proper screened dizzy cap.
Try GSF, Eurocarparts etc., but remember to allow for the cost of postage and insurance to send your old unit back, and be prepared to wait a while for the return of your surcharge.