Hi Randy,
Late to the party here but I'm staggered that, more than twenty years after T160 electric-starting problems with
Boyer-Bransden e.i. were thrashed out and solved on Triples On Line, there are still long threads about the problem.
Thick cablesBetween
battery -ve, solenoid and starter and between engine and
battery +ve - I don't see any mention of these in your thread? It's well-known standard were under-spec'd; they should've been checked - and replaced if necessary - long before you "hammered", "stood on" or "claw hammer"-ed the starter (Jeez!

).
If your bike's cables are ~5/16" o.d., chances are they're either original or poor copies:-
. Here in GB, I can buy cable known as "196/0.40" - 196 strands, each 0.4 mm. o.d., 25 sq.mm. total conductor cross-section, rated for 170 Amps. These are not "high purity" (wth is that?

), just bigger (~3/8" o.d.) and better-quality than originals.
. If you can't find something more similar, Dave Comeau (
Norton Board moderator) has posted in the past he uses 6AWG cable on electric-start Commandos (which have a higher starting Amps than a T160).
jumper cables are a cheap source for starter wires.
Expensive thick ones that'll jump diesels,

cheap thin ones that'll only jump gas engines,

Btw here, to amplify another of Dave's earlier answers, afaict T160 starters don't draw much more that the ones he sells - highest draw I can remember seeing from a
Lucas starter was ~160 Amps.
Boyer-Bransden Transistor Box and ignition coils wiringOnce you're sure your bike has decent electric-starting cables (not forgetting the short one between solenoid and starter), ime
don't wire the 'ground' (+ve) side of the
Boyer-Bransden Transistor Box or coils series exactly like the diagram @L.A.B. posted:-
. connect the Box Red wire directly to the
battery +ve terminal;
. either connect "Ignition Coil 1" +ve also directly to the
battery +ve terminal or at least into the bike's existing harness Red wires' network, at a snap connector.
Btw1 here, you might want to consider a lower-rated fuse (5A or 7.5A blade) in the Transistor Box -ve, say where the Box White wire connects to the harness White/Yellow from the handlebar kill switch? Otherwise, the only 'protection'

the e.i. has is the 15A or 20A main fuse.

Btw2 here, the link @L.A.B. posted:-
... is corrupt:-
. if you look at
B-B's Fitting Instructions index webpage, Code "KIT00054 (BOX00021)" equates to Description "Micro MKIV/MKIII ignition for Triumph Trident T150 / 160 and BSA Rocket Three Motorcycles.";
. however, if you click on the link @L.A.B. posted, the displayed fitting instructions are for B-B's MicroDigital e.i. (Code "KIT00085 (BOX00036)" in the index);
. the negative-side wiring is the same but KIT00054 (BOX00021) fitting instructions include an additional colour wiring diagram showing the positive-side wires connected into the bike's existing harness Red wires, similar to my advice.
I notice voltage drops to 10 when pushing the starter button.
Where are you measuring this? With your meter leads connected one to each
battery terminal? Or one meter lead connected to
battery +ve and the other lead connected to the connection between Box White and harness White/Yellow? Risking telling you something you know already, you should make both measurements with ignition and kill switches turned on, to ensure there isn't Volts drop between
battery -ve and the Box White wire.
Ignition coilsAnother thing I don't see in the thread is checking the coils?

If you haven't done it before, set your meter to Ohms:-
. Primary resistance is each meter lead end on one of the spade terminals secured by a nut; 'original
Lucas' (as fitted to your bike when new) were/are usually ~1.8 Ohms, common replacement PVL can be up to 2.2 Ohms; the ones you do
not want are the current Wassell
Lucas with 5-Ohm

primary resistance.
. Also check resistance between each coil's HT terminal and its LT (spade) terminals - should be about 5,000 Ohms but old PVL can be up to 7,000 Ohms.
. Finally, check between each terminal and the coil casing, should be tens of thousands of Ohms.
Having ensured decent electric-starter cables and decent ignition wiring both -ve and +ve and 'good' coils, the '6V' might now work with electric-starting for you - they have for many T160 owners over the years.
If they don't, consider '4V' coils; fwiw, a number of T160 owners have posted over the years both here and on TOL that '4V' coils with B-B has worked for them. Otoh, I can't remember a post by anyone actually using "capacitor-'n'-diode"?

Fwiw, never been impressed with three '6V' coils in series on a triple, but then I've always been a
Lucas Rita (three '4V' coils as standard) user.

The reasons Bransden has always used '6V' coils were two-fold originally:-
. When the only competition to B-B was Rita,
Lucas supplied three '4V' coils for triples but, as they made the coils,
Lucas were hardly going to supply their main competitor ...
. While Bransden had to supply replacements for T150 and Rocket 3 '12V' coils, '6V' coils - even
Lucas - were always easily-available; however, T160's came with '6V' coils as standard, so Bransden could make his e.i. look cheaper than Rita.
However, Rita hasn't been available new for decades, but '4V' coils are now easy; given the well-known problems with three '6V', Gk why Bransden continues to recommend 'em.

As I say, never known anyone actually do this ...
Firstly, the capacitor is
across the battery; i.e.:-
. Capacitor -ve must be connected in a wire connected to
battery -ve - I suggest around the connection between the Transistor Box White wire and the harness White/Yellow?
. Capacitor +ve must be connected in a wire connected to
battery +ve - I suggest an existing Red wires' snap connector. But not "any ground" - "ground" is simply an electrical conductor between
battery +ve and another component; like the Transistor Box and coils +ve connections I've advised above, make it a good one (not some crappy connection to some random bit of bike).
Imho, no. Use bullets into snap connectors - if this idea turns out to be crap, you don't want messy soldering to clean up particularly in the supply to the Transistor Box -ve; bullet 'n' snap connectors, you just pull the cap's bullets out of the relevant snap connectors.
capacitor as close as possible to the Boyer.
Afaict, the obvious connection seems to be around the existing connection between Transistor Box White wire and harness White/Yelllow? However, I've also advised a fuse for the B-B and the diode has to be connected somewhere?
diode has which end (+ or - ) closest to battery
Educated guess says the diode should be between
battery -ve and capacitor -ve, to prevent the capacitor's discharge towards the
battery.
If so, that's on the end of the harness White/Yellow wire, between it and the capacitor, and the White/Yellow is connected (through the kill and ignition switches) to
battery -ve ...?

Hth.
Regards,