@ g,i,lumens : Thanks , 1967 was indeed a good year .., it produced my wife !!!( I'm a little older , 1958 !...) And you assumed right , this is the way the hall sensors are working . The only weakness of those , is that the distance between the magnet in the ring and the hall sensor should be very small ( about the thickness of the tube ) , otherwise...Just as an example , I opened once a Niwalker Vostro BK-FA 02 , with rotary ring , in order to mod it , increasing current to the MT-G led.., changed the resistors , assembled it back and..., no light at all !!! Opened again , everything seems to be in order , no shorts , all the measurements were ok !..., and I decided to test the driver outside of the light , on the bench . Surprise , with a small , but strong magnet , at about 5 mm close to each hall sensor the light was doing what it suppose to do , on , modes , off... Then , I noticed that the sensors were SLIGHTLY bent towards the center of the driver.., I straight them back , up to the point where , inserting the driver back , they were touching the metal body ! That was the solution , everything came back to normal ! So , for these sensors , 1 mm counts , and for sure , the magnetic field generated by the magnet is important !!!

@ firestorm : Yes , this transistor could be replaced , there are , lately , a lot of good fet ... The only problems are that you have to identify it , check the specs , and find the original or better one ( higher drain current , lower Rds on ) , in the same case ... and to have the ability to desolder and solder small components ...

A soldering station , with hot air will help a lot ...

The idea is , that after you'll take out the old one , to check again the resistance between + and - of the driver ( as you done it before ) , and if the 17 ohms resistance is gone ( and you measures will be in the ranges of kiloohms , as was discussed here , earlier ) , you found the problem and you can proceed to order a new transistor ...But , if the " short" persists after removing the fet , there are some other possibilities for a short as : a defective capacitor , or MCU ...

I suggest you to take out the driver ( do NOT forget to make signs with a permanent marker ) , take some quality photos , of the both sides , so we could see and , eventually identify , the components , and guide you thru the process .

I'm sorry , I do not have this light , to open myself...