Ign light on, engine cut out

Well, a 7 year-old battery is getting on a bit. Depends how well you've looked after it.

But that 12.42 volts, is that with the ignition on? And that's after standing overnight, on the bike, ignition off, not on a charger?

Are you running original rectifier & zener diodes & generator light assimilator?

How many volts do you see with the engine running? Lights on or off?

What happens if you charge up the battery and run with the lead from the rectifier disconnected, i.e. total loss? Obviously the red light stays on but how does it run? Should go for an hour that way if the battery's any good.

Oh, there shouldn't be any "banging and rough running" just 'cos it's been ignored for a couple of weeks. And if you have water in the fuel you really should do something about it.

Good enough answer Stan, a reasonable well charged battery will be good enough for 50miles at least-no charging. IF the rough running is due to low/non charging then putting the lights on will usually kill the engine at tickover.
You could replace the reg/rect with a straight original type rectifier, short ride or with lights on would be ok It would be worth while watching the voltage.
I can check reg/rects (send with £5 for return postage).
The original type warning light assimilators can go faulty and they can 'take out' reg/rects.. Also check new stator for shorting to earth.

Michael, unfortunately the Reg/rect is the most likely to be at fault here. Deal with that and the assim first.

... suspect the battery especially as you say you've had to add water. I don't use wet batteries at all these days as the AGM type work well and don't spray everything with acid if mistreated.

1. If your machine has a working electrolytic capacitor with a charge, it should start and run (with lights if required) even without a battery in circuit (section J24 of the Workshop Manual; a test procedure is given). Note that currently supplied new capacitors are a different diameter to the original and thus require a corresponding new spring. N.B. also: they MUST be mounted with the terminals pointing downwards.
2. Replace the inept assimilator device with one of Al O's battery status monitors.

I have batteries that nearly ran dry and were too low on voltage to allow chargers to work and yet still work well enough now. Suspect something else first.

There is a whole raft of issues here. The only sensible solution on the MK3 would be start from the beginning. Get the tank and seat off and check through the loom inspecting the cleanliness of each connection, and item fitted to the loom, not jus the mating part part but the crimped portion as well. Junk the battery it's dead, at 7 years old it has had it. Next check the charging circuit (if bike can run well enough to raise the revs) Then add in each load and see what happens. 
The capacitor is a red herring and with modern rectifier regulators and the large battery on the MK3 it is not needed. It has been the result of two failures on my bike causing breakdowns, now it's gone. 
Water in the fuel? if there is and it's easy to spot then try and get rid of it. It should also have no interaction with the ignition light. The fact you may have water in the fuel suggests that the fuel is way past it's best. Unleaded fuel with ethanol should leave carbs squeaky clean, there should be no reddish brown residue left in the carbs when they have been standing like that seen in the 4* days. 
Personally I would not set out chasing one potential issue at a time here, just bite the bullet and give the bike a good going over whilst the seat and tank are off. 

If you start with a new battery you might just say' all is well' and not get to the real problem. The capacitor can be a red herring (or even a sprat!!) the new ones are in deed small in size but they do NOT need their terminals pointing down ward, Early idea from LUCAS)
Listen to Ashley, check all the rotten wiring, (yes it is rotten if it is original 50yrs old!!) check battery charging voltage-any doubt send the reg/rect back for testing, recharge battery with a proper charger (not one of those silly automate things). Perhaps replace reg/rect with a straight rectifier?
All done.

Whilst you're checking these things have a look at the ignition switch.  My 1976 Mk3 Commando died suddenly in Aberystwyth, restarted, then cut out again.  This turned out to be the ignition switch, but it worthed fine when turned to have the side lights on.  The contacts within the switch were the problem, they only lasted 47 years!