Pre MOT check

Well the washers and wipers fine , next the lights all ok apart from one headlight ! I have been putting this off since I bought the Griff went out and got myself some axle stands and a trolley jack ,anyway took the light cover off all looked ok so took the bulb out and tested it on a PP9 and it came on ! if a little dim so off to Homebase to get a multimeter tested the earth to live and it shows about 11.6 volts ? so back to Halfrauds to get some new bulbs fitted the new bulb and you guessed it nought .
Not being an engineer or an electrician I'm stumped , any ideas gratefully received , Rgds Simon

Taking it to local garage I have used before , it didn't work with original bulb and not with new either , battery a bit low I presume because I keep checking the lights without the engine running and it still starts the engine fine so cant be that much wrong with it ,the battery that is ,Simon

Thanks Sardonicas for your input , but what 3 pin connector , I just have a couple of spade connectors ? Rgds Simon