[Ian M Davis]

If you are measuring >12V at the clutch plug but are unable to light the bulb it suggests you have a bad connection. Digital voltmeters have a very high input impedance so don't load the circuit. If you were to measure the volage with the bub connected you will read a low voltage.

 

[Ian M Davis]

Hi, yes it could be a bad relay but if it supplies 12v then it should be good enough to light the bulb.

No that is not necessarily the case. If the relay contacts are making a bad contact and for example if you have a resistance of 1000 Ohms (1 kOhm) and you connect a meter with an input impedance of 1000000 (1 MOhm) for a the supply voltage is 12V the meter will read 11.988V.

 

[Ian M Davis]

My car is in a public garage and I there is not room to dismount stuff really. I just ordered the connector to easily be able to connect to the clutch and do resistance measurements and external 12 V supply. But thanks for the advice.

If you have the bulb connected in parallel with the meter and the meter reads 12V but the bulb doesn't light then something is wrong with the bulb.

EDIT
Can you test you measurement set up directly on the car battery?

 

[Ian M Davis]

@Davehuge and @Ian M Davis, until now I used a normal household 230 V bulb, maybe I should swap to a car intended 12 V (Amazon.se) ... Said and done, now it lights up!

230*230/21 gives 2.5 kOhm, compared to 12*12/55 2.6 Ohm... Could this be the reason the normal household bulb is not able to lit? The lamp is to be consider a resistor, and with 2.5 kOhm and 12 V there is very little current able to pass, giving only 0.06 W?

Picture for proof, and thanks for the support. I will try to get the coil (or is it both clutch and coil?) replaced!

Yes that's correct. It never occurred to me you were using a household light bulb. As a matter of interest what type of bulb was your 21W 230V house bulb. 21 Watt is quite low for a tungsten filament lamp and quite high for a LED light.