I do have an amplifier after all
Boyer Bransden Micro Mk3
Just so you know, Bransden call the 'box' a "Transistor Box" and the two parts of the 'trigger unit' "Stator" and "Rotor".
someone’s already done some wiring for sure!
Your other images show - apart from one or more past or present severe oil leak(s)
- a PO's stripped the original loom and then done a not-unreasonable job of organising the loose wires by grouping them with short lengths of the red insulating tape. Just a shame about the colour-matched squash-on "bodger's terminals" ...
Imho, degrease the bike, cut off the bits of red insulating tape, it looks quite an easy rewire.
If I'm rewiring a bike I haven't done before, and the old loom's still connected, I start by using a sharp scalpel-type knife to cut away any wrapping; once the loom's visible in Glorious Technicolor, it's much easier to make sense of the any wiring diagram's black lines
What do you do with the handlebar switch wiring
If they work, usually nothing; at most, I might change the terminals on the ends of the wires.
As part of my first rewire - of one of my T160's - I had planned to fit (a) more powerful headlamp(s), but I'd also planned it/they would be switched by relays. In that case, undamaged original wiring and switches are more than adequate to to conduct the relay switching Volts/milliAmps. If you aren't planning more than a single 60/55 headlamp bulb, it's debateable whether headlamp switching relays are necessary, but I always incorporate them anyway.
have a splayed head T140V type head ready to go on.
You are aware:-
. It might not be a simple head substitution? Tappets, tappet guide blocks, pushrod tubes and seals are all different between T140V and '81 T140E.
. Spark plugs need to change from T140E Champion N5 or equivalent (NGK B6E-something?) to T140V Champion N3 or equivalent (NGK B8E-something)?
head in the photo is the original parallel inlet T140E type but with Mark 1 concentrics fitted.
Just a thought but I wonder if that's one of the brackets one of the US importers used to offer as an accessory? The parallel-inlet-port T140E head is based on the basic single-carb-head casting, for which at least one of the 1960's US importers made a bracket to bolt twin carbs. to the the twin ports.
Unless you've an overwhelming desire to fit the T140V head, and/or having two Mk.1's that close together is a pita, the existing set-up's something unusual ... If It Ain't Broke, Don't Fix It?