What Trade skill would you need to have to make electronics, like vox-casters or halo projectors?

Probably Trade (Technomat). It's the generic 'I build/maintain/work with technology by rote but don't know how it works' trade that might apply to a factory worker.

You'd need an appropriate common lore, tech-use, or something similar to actually design the things, or else be working from an existing plan, though.

I believe you actually use Tech-use to build electronics.

The various tech/trade skills are a real mess. I've tried to make sense of them before, and this is what I've landed at:

(From my House Rules for using OW rules with BC)

The various skills have different focus, and work together with certain synergies.

Common Lore: (OW, p120) The GM can call a player to use the Common Lore Skill when:

• The GM feels the Player Character might know something about a current situation, location, or individual.

• The character wants to know a specific detail about a common subject.

Forbidden Lore: (OW, p121) A successful Forbidden Lore Test imparts information from the GM to the player.

Common Lore (Tech) lets you know which litany or ritual is appropriate to common situations. It does not require any technical understanding, nor does it provide any benefits when dealing with uncommon situations such as interacting with an ancient archeotech cogiator device discovered on a derelict hulk. This is the application of Rite and Rote learning to operate tech, and is the way the great masses of low ranking tech-priests operate. It will let you identify machines of Imperium and Mechanicus design, revealing details such as pattern, manufacturer, model, as well as trivia about the item and its history.

Common Lore (Machine Cult) is knowledge about the overt elements of the Cult Mechanicus. It covers such things as "the symbols and practices of the Mechanicus, as well as such things as formal greetings and identifying ranks". It has no practical application when it comes to operating or maintaining tech, but will prevent you from making a fool out of yourself when dealing with Tech priests.

The Forbidden Lore (Adeptus Mechanicus) has no practical application. It does not cover secret knowledge of plasma drives or the truth about the nature and existence of Machine Spirits. What it does cover is "An understanding of the followers of the Machine God, including such things as their observances, common beliefs and core philosophies."

It might be useful when interacting with Tech priests, trying to understand their motives and/or actions and perhaps to evaluate whether or not something is orthodox or not. It does not help with obscure tests to work ancient cogitators, but it might help trying to decide whether a suggested repair/modification would be acceptable to the Mechanicus or not.

Forbidden Lore (Archeotech) will let you identify the nature and function of ancient devices you find. It might also help with the test to operate the ancient cogitator, but is once again a skill with little practical application. It will not allow you to recreate ancient las-pistols of incredible power, or allow "creative" designs to improve your plasmagun. "No Acolyte, however skilled, can create or repair weaponry from the Age of Technology." (IH, p 240)

Building or modifying weapons, gear and other tech is covered by Trade skills. Tech Use alone does not let you do this. Attaching weapon upgrades is covered by the Trade (Armourer) skill (Core book, p141). Making a primitive plate armour is covered by Trade (Smith) (IH, p243), while the usage of less primitive elements would require Trade (Armourer). To create structural component, or armour plating for a vehicle, Trade (wright) is also needed. Neither of these skills will let you invent anti-grav plating or teleporters, you will need blueprints (preferably based on an STC) or you will be stuck to making rather primitive things.

Trade (Technomat) is “used to maintain and repair technological devices, but through rote memorization rather than true understanding” (OW, p134), but it will not let you build them.

It does not indicate an understanding of the tech they work with, but they do know to spot a faulty flux-capacitor and to replace it. Should the flux-capacitor require extensive repairs after the unfortunate application of an evsicerator or Choppa, and they have no spare part to replace it with, they might be stumped. It will also let you operate ancient machinery, even if nobody knows how they work: "The Skill may also be used to create effective rituals for newly discovered items, based upon the vast knowledge of customs for similar devices. Thus, if the Acolytes discover an ancient cogitator, their technomat might attempt to placate its machine-spirit with rituals known for similar machines." (IH, p 244)

Tech-Use would let you repair the Flux Capacitor, however this would be a very hard test unless you have the relevant blue-prints and/or specialized knowledge. It is more commonly used to repair and operate mechanical and electronic items, and represents your ability to tinker and "figure things out" like a proper grease-monkey and geek. Designing a replacement for the Flux Capacitor based on available material would be beyond the scope of this skill. Indeed, it appears to fall outside of all the skills described in the book. It seems to just be "not done".

Tech-Use does not mean understanding of HOW the technology functions, it will just let you operate and perform repairs on it. Like the computer technician who knows how to replace a faulty motherboard, but has no idea about how to make a new CPU, or how it works. The scope of work you may attempt to do with Tech-Use is limited to your knowledge of technology and any instructions and/or documentation available.

Logic is the theoretical counterpart to tech-use, and represents understanding of mathematical and mechanical principles. For Tech-priests it also covers Mathemechanica Rituals, granting bonus to certain Tech-use applications.

Very impressive hous rules!

But in short, it doesnt answer the question. You kind of could use Tech Use but only with blue prints to build a vox box (a radio), but with Trade Armourer you can build a las pistol from scratch. That doesn't compute.

And in TLW p. 58 it states that you need Forbidden Lore (Adeptus Mechanicus) to build integrated weapons so it should give some secrets to the trade.