Yes, you could get away with a t joint as long as you can insulate it suitably. Can't comment on silweld, never used it.
There is no real need to take multiple drop wires, assuming the one you tale off is enough to supply all your equipment. Be aware the current you are talking about here is prior to the dc converter, so a lot lower than the current to the lights.
If you tell us exactly what you are supplying, and power consumption we can tell you min cable size. Alternatively, over spec it. 1mm diameter is good for over 10 amps!
Fantastic - I can tap the drop wire then rather than the main one ? Will have different circuits at different voltages (9v, 12v, 3.7V at the moment - will be clearer when I can see exactly how to get the lights to work and the voltage I am allowed to run each of them at). Thus need to multi-branch the feed to a number of DC-DC converters.
......
The salvage instinct in me is kicking in now ... I have a perfectly good 3 x CREE T6 light which at present runs off an 8.7V battery pack that has a damaged lead on it rendering the light pretty much useless for now. It’s this light :
HOT 3 x CREE XM-L T6 LED 4000LM Bicycle bike HeadLight Lamp Light Headlamp | eBay
It would be fantastic as my “high-beam” light for flashing at undipped headlights if it could be modified for wiring in, and I already have the diffuser and a mount for it. One little flasher CREE T6 on the handlebars I could fit, the single CREE running lights could go on a bracket on the front forks.
Have found this driver after much googling :
$4.5 | 22MM 3xCree XM-L T6 emitter Led Driver&led circuit board(2*18650,8.4V,2500mAh) Worldwide Free Shipping!!!
It doesn’t look like it’s a multi-mode clicky switch one. The only 3-LED driver sold separately I’ve found after much searching. Took the bull by the horns and ripped open the light to reveal its inner secrets :
Both the battery wires and the single-LED wires are accessible, unlike the single-CREE LED light I have which is pretty much sealed in.
So tentatively, if it is a single-mode driver my thought is to wire it in using the 36V to 9V step-down converter tillson linked, which is rated to 3A, and to swap out the driver board in the light for the new one.
From everything people have said in response to my many threads & posts trying to work this out

o), I presume this should work ?
I can then have my light unit at least for a flash-beam and a 3-cree is far more suitable for this than a T6 single LED run at 1400mA. I’m guessing the LEDs in the light unit are arranged “in series” ?
Cost would be $25 with postage – not much more than buying a replacement battery pack – but I could get driver boards cheap for my other LEDs at no extra postage.
Am thinking I would then just (!) have to swap the driver board, cut the battery pack connector off and splice in the new wires from the power supply (I guess over the handlebar switch so flicking this to setting 2 of a 0/1/2 could turn them on ?) ... can’t see how that handlebar switch wiring would work yet but would be great to know it could be done in principle ...
Handlebar switch envisaged is this one :
Handlebar Switch - 3 position lights plus Horn/Kill | eBay
The lights off switch setting 1 would run at a different voltage and be supplied via a separate DC-DC converter.
I’ve sent the supplier of the driver board an e-mail asking for confirmation that the driver board is single mode (hopes !!) but they’re off-line till Monday.
Could this be the light at the end of a long dark quest ?