Firstly, welcome to the Forum.
Once it runs reliably, up to you how much additional farkling you want to do.
However, has the bike been unused for any length of time?
Be aware the Haynes manual in your photo. is great ... as a doorstop, under the short leg of wobbly furniture, firelighting ...
The Triumph workshop manual is both free to read online
and available from 'Meriden Triumph' (i.e. not Hinckley-only) spares dealers.
(and it's a J-Lo) your middle photo. suggests you have a T140E
(Amal Mk.2 carb.in the photo), looking at the engine and frame number will confirm.
If you do have a '78 T140E, be aware there isn't a published wiring diagram for them anywhere and some of their wiring is different, it is not the same as any wiring diagrams in either the Haynes or any Triumph manual
so don't become confused by them. Fwiw, I'm familiar with both T140E and T140V wiring.
Also use the Forum Advanced Search to find threads started by @Lake Marine
, he's recently got another '78 T140E going.
Firstly, do you have a multi-meter? If not beg, steal or borrow a good one. Good meter's as essential to working on electrics as good wrenches are for working on nuts and bolts. If you have to buy, a "good one" has a well-calibrated meter and a cast-iron guarantee it has EMI (electro-magnetic interference) protection.
Secondly, does the bike have a 'good' battery. Doesn't have to be new but, whether it is or it isn't, your good meter must display:-
. 12.6 Volts when each meter lead is connected to a different battery terminal and everything on the bike is turned off;
. no less than 12.5V when only the ignition is turned on.
Good meter, any less and the battery is not 'good' (usually) or there is a major power drain somewhere in the ignition circuit.
Next, unless the previous owner can confirm he (she?) never screwed with electrics "ground", wise to use the meter to confirm it. Original electrics were 'positive ground' - the battery +ve terminal is connected to the engine and cycle parts - but PO do change 'em ...:-
. meter still set to Volts, put the end of one meter lead on bare metal, other meter lead on first one battery terminal then the other;
. meter lead on one battery terminal, meter should display zero Volts, meter lead on the other battery terminal, meter should display 12+ Volts;
. the battery terminal where the meter displays zero Volts is "ground";
. if the meter displays zero when the lead end is on both terminals, move the other lead end to a different bit of bare metal ...
Assuming standard 'positive ground', any Triumph wiring diagram you look at (Haynes or Triumph manuals), the ignition circuit:-
. Starts with the Brown/Blue ("NU") wire from the battery -ve terminal, through the fuse (not shown?), past "RECTIFIER" and "ZENER" to "IGNITION SW.".
. Switched output from the Ignition Switch are the plain White wires, one goes to "ENGINE STOP" - as standard, Red lever in the switch cluster by the front brake master cylinder on the handlebars.
. Switched output from the Engine Stop switch is the White/Yellow wire. Wiring diagrams will show this going to the -ve terminal of each ignition coil ... but that's where the wiring changes for the EI ...
Boyer-Bransden fitting instructions applying
; however, depending how good you are with electrics, the wiring diagram isn't brilliant (Bransden has been selling his EI since the early 1970's, when most Triumphs didn't have engine stop switches, he's just never updated his diagrams to reflect the changed market
If your bike's electrics are still standard 'positive ground'
. As standard, the Mk.3 Box's plain White wire should be connected to one of the original ignition coil White/Yellow wires; the terminal on the other original ignition coil White/Yellow wire should be insulated - note this can be useful for trouble-shooting so allow access to it when necessary.
. However, I advise against two connections shown on the Boyer-Bransden wiring diagram:-
.. The Box Red wire should be connected directly to the battery +ve terminal, not to an ignition coil terminal.
.. The coil terminal should be connected to existing harness Red wires at a snap connector, not to "POSITIVE FRAME EARTH".