To summarise.
- front coils removed - presumably because trying to connect to the HT pin using aluminium foil did it not work?
- all 4 ignition coils primary/secondary coil resistance is within spec. so no shorts or open circuit hence all coils appear to be good.
- voltage at coils is 11.1 V - previously "I have measured voltage at the R/W indicated in the manual .... 10 .7 volts" - how did you manage to gain 0.4 volts? (not that it matters but higher is better)
- resistance for HT to spark plug electorode for rear 2 coils with leads and spark plug measure correctly - I would suggest you do the same with the front so you know connection is good before refitting. them.
- starter/turn signal relay is making a noise - this concerns me but it does not appear to prevent the engine turning over nor do I see that it should affect the TCI - BTW do the turn signals flash?
- according to the Haynes manual, pick up coil (ignition switched off when measuring resistance) orange wire to each of the other 4 wires should measure 94 - 126 ohm (I'm not convinced the manual is correct) but you get very different readings - so the pick up may be bad. (hooking a 'scope when turning enigne over would show a signal)
I have looked at the wiring diagram and see the kill switch and side stand relay connected so these act as a 'cut off' for the TCI.
The only way I know to check the TCI without 'sophisticated equipment' would be to connect a red/orange/yellow/green LED and 1 k ohm resistor to the coils - see below (note resistor value, indicated by colour bands, in diagram is not 1k ohm)
If you don't have a soldering iron, then use a terminal block and screw it all together. Note I specify LED colour - don't use blue/white since they use different semi-conductor technology so may blow if connected the wrong way round. A LED and resistor can be purchased online (e.g. ebay) or from Radio Shack if they still exist. When connected as per digram, the LED should be lit and when engine is cranked over, the LED will flash but it is quite hard to see. It may well dim as the battery voltage goes down when turning over the engine but the flashes, if they happen are obvious. You can't use a light bulb instead of a LED as they react too slowly so you won't see the bulb flash.
I would suggest fitting ignition lead and plug to rear coil, wrap wire around the spark plug thread with other end of wire connected to an earthing point - then turn the engine over - there should be a spark in the gap (like what you have been doing but with a solid ground for the plug). Actually this should be enough to test (no need for LED nor 'scope) since the coil/lead/plug has been checked out.
One of the coils has a lead to the tacho, so the tacho needle should move when turning the engine over.
Regarding 'sophisticated equipment' this would be an oscilloscope. I have this one (search multimeter ET828 on ebay - a cheaper monochrome version exists) for £ 70. This my seem a lot but it has an auto-ranging DVM that is probably better than yours.
I managed to capture the signal at the coil orange wire when cranking over - see below. It normally sits at around 11 V but is switched to ground by the TCI.
The alternative is to substitute by replacing the TCI (I estimate this will be at least £ 200 or an after market version even more £££ - double that number ) and you may get the same result as there may be something else preventing a spark - note I believe Sean does a kit where you are sent various ignition parts to try out and then keep and pay for whay you need, returning the rest.
Sorry but don't know what else to suggest.
