you may be loosing oil pressure when the engines hot!
you need to have the oil pressure checked out..
it should be 2 bar with the oil temp at 80c i think i cant remember if thats at idle or at 2000rpm....... it will tell you in your haynes manual!
your engine will have 2 senders on it 1 on the side of the head and 2nd on the oil filter braket!
the high pressure 1 is on the oil filter braket and if the oil pressure drops below 1.8 bar over 2000rpm it trips the led off and a buzzer!
the other 1 does lower oil pressure so when you start it at idle the led goes off! this switch made the led flash when your first turn the ignition on!
so i would say that this sender is either faulty or sensing low oil pressure at idle! low pressure at idle is not uncommon in high mileage engines!
they say low pressure at higher rpms is more of a concern!
have you got any oil in it! this can do this!
so i'd check your oil!
most people dont check there oil and this is what causes engine damage! trust me i know been there done that! ive learned! i check my oil all the time
thats why my gti has done 211000 miles on factory engine! its sitting on my drive with a busted gearbox!
and the engine still starts first time and ive not been using it!

vw engineering
if your oil levels ok and you look after your car oil changes etc... then i would get the oil pressure tested!
if its? normal then replace the sender! as this could be faulty!
basicly the switch on the head is always earth hense the led always flashes until? you start the car up! and then it disconects and the light goes out!
the other sender gets earthed when the oil pressure drops so this makes the led light flash and a buzzer come on!
so the earth switch in the 1st sender on the side of the head may be worn and earthing resulting in the led flashing!
but before doing anything else get the oil pressure tested! if it turns out to be low then it could be a worn oil pump or worn bottom end or a blocked up pick up tube!
it could also be that the pump is worn and the oil is getting too thin when hot!
there may be nothing wrong with the engine mechanicly is could just be the wrong grade of oil! what oil are you using! or it may be abit of this and with a problem ive suggested!
worst case sanario is your engines worn!
but is you have done oil changes and checked the oil levels your engine shouldnt really wear excessively!
like i say most people let there oil drop below minimum!
this fcuks the whole engine top end cams tappets valves!
and as the oil get lower it starts to take away the piston rings and then the pistons and then the bottom end the big ends the main bearing the oil pump! etc!
i hope this helps!