Well... After locating a magnifying glass & using a better source of light, I was able to just barely make out the tell-tale sign of the Phillips pattern way down inside the reset knob. There is no way that I have a Phillips screwdriver that small. Were talking eye-glasses screw type of small. Fortunately I do have a small set of jewelers screwdrivers, but they are all flat blades. Luckily the screw wasn't very tight & I was able to back it out with a very small flat blade screwdriver.
Now for all you Ascot owners out there... I recommend that you go right out to your bike after reading this & try to wiggle your trip odometer reset knob. If there is any play in it, you may want to try & remove that screw. Then put some Lock-Tite on the threads & tighten it back up. Be very careful not to drop the screw, as you may never find it again.
Good luck
J.