On the various points arising ref the mag . . . my ha'penceworth . . .
The cam lobe that is about 4 or 5 o'clock looking at the points end-on always fires the HT pick-up on your right - the rear, gearbox side, one. The points will be at about 10 o'clock when the heel opens them on that lobe.
The lobe at 10 o'clock-ish fires the front one.
Which plug lead you connect to which pick-up doesn't matter at all as long as you know which cyl is on compression when you set things up. I always have the rear pick-up to the rh plug on my bikes, many prefer the left.
TT's bit 'o brass should be visible in the appropriate pick-up hole when the points start to open - if you can get them off. If the screws on the pick-ups don't have hex heads for a spanner, as they should (as well as slots for a scrooge), it can be darn difficult. They are a fiddle at the best of times on the bike. The threads are also a bit feeble - so careful with the weaponry, as it's not a simple fix when they are stripped. They are often damaged, sometimes fubarred - and there isn't a lot of metal for a 3BA thread insert.
There are 3 basic sliprings for Lucas mags with rotating coils. 360° brass for singles and 4+ cylinder mags with distributors, and twin types with a single segment about 90° of the circumference. Where precisely the segment is embedded in the plastic depends on the rotation of the magneto (or on which end of the armature the slipring is fixed). The camring position is different according to rotation - that is why the brass has to be in a different spot, but 90% of Brit parallel twins are Anti-Clockwise drive and use K2Fs. Exceptions are some few Royal Oilfields, and I think maybe Douglas and another 'minor' marque I can't recall off the top of my head.. Vincents are all clockwise drive. Exactly the same variations are to be found with BTH or other marques, depending on rotation and internal construction.
While there are some dodgy sliprings out there, most that are fitted by repairers of these things are of decent quality and UK-made - the problem with carbonisation of the thing, if it's a decent one, is usually soft brushes (see posts numerous on here!)
Camrings are different for manual and fixed, but only in the sense that manual ones have to be notched for the movement of the ring, and for the plunger that moves it. Fixed ones just have one notch, a small one. If the ring is badly positioned with ref to the armature, it might account for weak sparks if retarded, or no sparks if over-advanced. The points want to open JUST after the 'flip' of the armature, at full advance. If making notches - extreme care needed - and going at it willy-nilly will lead to woe. However, the rings are symmetrical on a 360° twin so in the worst case - if there's a problem - it can be rotated 180° and new notches put where notches need to be.
Resistances - the low tension coil has a resistace of about 0.55 or 0.6 ohms typically. Because that is pretty tiny, you'll not be able easily to tell when points are open or shut using a battery and bulb. You can measure the low tension R by sticking a meter across the points with them open. A low tension failure, other than a broken wire problem very occasionally at the condenser end, is very rare.
A meter from a plug lead to the mag body should show the resistance of the HT coil, about 5000 ohms typically, when the HT brush attached to that HT cable is 'on the brass'. Ie for about 90° of the rotation of the magneto only. When off the brass - nothing shows. That 5000-odd should show up whatever part of the mag you touch.
If there is no HT resistance reading at any position of the mag, then one of 2 things has happened. Either the connection of the coil to the slipring is bad (it often can be after a mag has been taken apart, it's not a great design), or, more likely, there's a break in the HT winding. A small break won't stop the thing sparking on the bench, and quite often it will run the engine for a goodly while. Until arcing makes the break too long for the spark to hop across it plus then fire the plug.
Any loss of HT continuity needs to be looked into - because a call to the breakdown service, or to a mate with a van, is only a gnat's cock away.
Coming back to the total failure to fart or bang, it does seem possible that the mag isn't sparking under load, because even if the timing weren't that close to right, or the camring were off its optimal position, you'd expect a bang now and then. I'd see whether the spark in free air can jump a decent 1/4 inch at kickstart speed by holding a bared HT cable that distance away from the head or whatever. Sparking a 20thou plug gap in plain air is not a good enough indicator unfortunately. But of course, could be valve timing, or a carb thing, or summat else altogether. Tis a process of elimination!