***Before messing with ignition, try spraying premix fuel (50:1 ratio just like in your tank) in the carb opening and in both spark plug holes. If it starts and runs some then you have fuel delivery problem and may need to go back and look at your fuel system. If it doesn't start then proceed below. (but still check quality of spark on both set of wires)
Please check the spark on both cylinders. Get a spark plug tester($6 or $7 at just about any auto parts store) and look at the quality of the spark. The gap should be set to about to 5/16 inch and there should be a good sold blue spark. If there is a weak or no spark then inspect your wire going from the plug to the coil and make sure every thing looks good.
---I will tell you, I have read a bunch of posts and articles that the coils made in the 60's had issues with the sealing and often plague people. Changes with OMC's coil covering was done there after. Any way, you could be having a problem with the coils. While your under the flywheel checking on the coils, consider getting a tune up pack with new points and condensers. (Tune up pack is about $15 or there about. Good piece of mind that you will not have to worry about going out or giving you problems on the lake. Condensers can go bad.
---If there is no spark or weak spark, try the tune up pack with points and condensers first, then if there is still no spark then the coils. You don't have to get OMC coils.....Sierra work fine.
---After sanding the points, did you clean the points well and gap them at 0.020 with a feeler guage....if not the gapping could be off and no spark or very weak spark.
--- You stated you had it started and it ran for a little while, so your close and I know frustrated.....been there too. Have couple of beers or step away from the motor a couple of days and regroup.
Hope this helps you some.