Im guessing that for 1961 it was a distributer model (not side points)? I am not familiar with these distributers in the slightest so bare with me, if you have any photos they might also help.
I agree with Gunner, its most likely a broken/loose connection or one made in the wrong place.
check with a multimeter that you have a good connection between the points in the 'dizzy' and the + side of the coil, check also that the condenser is grounded sufficiently on the engine and the screw firmly fastened, also that the other wire is connected with the points (or if the condenser is not mounted at the points, but near the coil, make sure the body has a good ground again and the lead is attached to the + side of the coil.
check again with multimeter (set to ohms on all of these, or buzzer setting to save you looking at the meter if it has one) that the points do not have conductivity with the motor, so put one lead on say cylinder head fin (easier if you have leads with crocodile clips) and the other onto the sping steel on the points. when the points open the buzzer should stop or resistance should show "I" (infinaty) or far left on a dial/analoge meter. if you turn the engine over the points should then touch eventually and this should give the opposite effect showing continuity.
The WSM shows this using a battery
and a lightbulb but in effect is performing the same function.
If this happens, connect a lead from the battery
directly to the negative side of the coil. this bypasses the complete loom.
fit the plug into the plug cap and rest the plug on the head. turn the engine over and you should see a spark. timing at the moment is not crucial. Although it will be to start the bike.
you can then remove this wire and go through the loom and see if the spark happens again. If it doesn't then you need to find that wire in the loom, a long length of wire and going between different points and testing will help, alternately check the continuity of the wires as you work through them.
I mention checking the points first as if you don't have this bit sorted under a simple circuit then you could spend more time at the loom and still be sratching your head.