Number one... The Fuelsaver MK2 is balanced flue, which means to change the thermocouple or overheat stat requires removal of the combustion chamber which should only be done by a registered CORGI Engineer as per the Gas Safety Act 1998.
Number two... Yes, the gas valve can be checked (To a limit)... The gas valves on these use an electro magnet which, after time does loose it's ability to stay first off, ensure you are using a high quality thermocouple; long life ones will usually conduct the voltage much better, then try linking out the overheat stat FOR TESTING PURPOSES ONLY (Do not leave it unattended whilst linked out) to ensure that the overheat stat is not causing any additional resistance to the conducting circuit.
Check and clean the pilot, make sure the injector is clear of any debris and that the pilot is of adequate size and is fully playing on the thermocouple tip...
If; after a 20sec waiting period the gas valve is not holding open, you will need to make arrangements to have it changed and the new one setup...
I do beg people not to try and skimp on gas fittings, we know they're not cheap... But these things can kill if done incorrectly.
GasAid.co.uk, December 2006