Hi Eli,
thinking of drilling a couple of holes for the idiot lamps between the gauges
As you intend to use the bike year-round, bear in mind the electrical connections will be out in the rain and spray coming at the front of the bike.
Your bike's headlamp shell is a modified '71-'78. Originals have only the lighting switch hole and three idiot lamp holes; your bike's shell has had the centre idiot lamp hole opened out for the Ammeter, is why the remaining idiot lamp holes are so close to the Ammeter.
The downside I found with the correct pre-'71 shell is it only has one wiring hole in the bottom. Not a problem normally on pre-'71 Triumphs because they have few handlebar switches to be connected and don't have indicators. However, when I build a loom for a Triumph, not only do I split the wires to/from the frame, I certainly wanted indicators on my T100. That'd come with a '71-'78 shell, I thought about modifying it for an Ammeter but instead decided to replace it with a correct pre-'71 shell and have two more wiring holes in that.
View attachment 774030
mystery wires... White is an ignition live, the brown an earth.
Uh-uh, you're confusing Brown with the unswitched '
not-earth' on other British vehicles?
On bikes, while White is still switched by the ignition, Brown is only to the rear lamp brake filament from its switch(es). As those two connections are by the top yoke, they're for the front brake switch, which was built into the cable as standard.
Tr6c NO kill switch connections?
If you're looking at the correct parts book for a '70 UK & General Export 650 (99-0901), the TR6C was still a US-only version and, although the kill switch was more widely-available and fitted than just to the TR6C, it's only illustrated/listed on the TR6C pages of the '70 US 650 parts book (99-0903 Part 1, pages 76/77). It's a push-to-break button, two White wires (originally), connects at the bullet connector in the White wire from ignition switch to coils -ve.
View attachment 774031
These two don't register anywhere, no ground, no power. I've tried with a multimeter and a test lamp.
Indicator wires - Green/Red is left indicators, Green/White is right.
They're even present in all original Lucas '70 looms; most '70 grabrails have mountings for rear indicators (7/16" hole in the triangular gussets between horizontal "lifting handle" and semi-circular passenger grab hoop behind the seat); otoh, the bikes lack front indicator mountings and looms lack the Light Green/Brown wire to connect indicator relay (positioned under the seat '71-on) to handlebar switch. I've never managed to discover what was going on during 1969 that left fitting indicators half-done.
View attachment 774032
The ignition warning lamp is a live feed and a ground so removing it shouldn't stop the bike from running.
Your bike doesn't have an "ignition warning lamp" ...
If you're using either of the wiring diagrams in the '63-'70 Triumph 650
Workshop manual captioned, "... all models from DU66246 ...", be aware your manual is (the common

) one missing the wiring diagrams "... from DU85904 ..." ('69) and/or "from HD23795 ..." ('70). These show the red idiot lamp is "OIL PRESSURE WARNING LIGHT" with a White wire and a Red/Green (i.e. not the left indicators wires) wire, the latter from the lamp to the switch in the front edge of the timing cover.
From your photo., would I be right in thinking dear Wassell have put a White/Red (electric-start ...) wire in your bike's loom from bulb to switch?
If you want a correct wiring diagram online for your bike, there's a small one in
the Triumph '70 650 Owner's Handbook or bigger ones in
the Triumph 350/500 Workshop Manual (identical electrics), "HH" addendum section.
can't find the connector for the speedo lamps anywhere (should be brown and green).
View attachment 774024

Wassell's 'quality control' ... The above photo. shows a Brown/Green wire straight from the main loom to a spade terminal of the lighting switch (left side of your photo.). That spade terminal should've had a second short Brown/Green wire crimped into it, that short wire terminating in a bullet; original speedo. ('n' tacho.) bulb wires had similar bullets to connect.
Risking stating the obvious, because the speedo. bracket's rubber-mounted, try for a bulb holder with both -ve and +ve wires or you'll have to run a separate Red wire from the speedo. to an existing Red wires' snap connector.
all squeezes in together. The relays both have 7.5A fuses.
Hth.
Regards,