I really should learn not to post until I'm fully awake.
The harness you want is part #99-7056 (TRIUMPH) or 54965505 (LUCAS). There is also a reference in the parts book to a rear sub harness #60-7198. I suspect this is for the taillight lead. Information is taken from the '79 Triumph T140E parts book #99-7102. Your bike is a '79
The other harness you mention #54962258 is for a 78 TR7RV,T140V,and T140E. These bikes were positive ground and had a points/coil /condenser ignition. It will not fit or work on your bike without MAJOR alterations.
The T140E model was a mid year change in the '78 model year. I suspect the first T140E was bulit in the Jan 78 (or very near time frame). The E in T140 refers to EPA. The biggest change between the '78 V and E models is the new cylinder head carb setup. Also there were other changes airbox, and styling covers, V model taillight carrier was black while the E model was ifin I remember was polished. The rear fender and frame also have different part numbers.
Now to your bike it is 1979. In looking at our posted picture it shows all the details of a '79
Seat lock, airbox styling cover and emblem, 79 and later front master cylinder, you are missing the lift rail which will have a small rack attached. Another thing for you to note is your rear brake caliper is underhung. On '80 and later T140E's the caliper was above the axle. The 80 model called a 79 1/2 in the USA for legal reasons is in part book 99-7102A
and starts with an XB vin. in reviewing the 79 vin history It appears they were built from
July '78 thru Nov '79 So they were built in both Oct 78 and Oct 79. Since you didnt mention an appromate vin if you have an Oct '78 bike I would guess you Vin is in a NA12XXX or NA13XXX range. If you have a Oct '79 built machine I would guess a vin somewhat like a NA22XXX or NA23XXX range.
Hope this helps