Logic is an interesting skill, and it seems like a good one. Despite that, I don't find myself asking for Logic tests much at all. What have the rest of you experienced? How often do you call for Logic Tests (that are not part of talent activation)? What kind of thing should it be called for?

Logic Tests are usually used in my group when dealing with the Adeptus Mechanicus in place of Charm/Diplomacy or other traditional social skills. Some people also go for them when coming up with a plan to see if I (as the GM) notice any discrepencies that their characters should be aware of.

If they're working at a mystery or tricky social situation and don't know what to do, I'll also usually allow each character a once-per-session Logic roll to try and figure out the next move (or at least the next move I want them to do), on the agreed condition that no matter the result, their characters will try to follow that advice.

Another thing is to remind your GM that you have certain skills. No one can remember anything everything, so when your GM asks for a test of some sort, and you don't have the skill (or it's linked to a really low stat), ask to change it out with another skill ( and with linked stat that you are good that at), which is relevant to the test at hand.

Edit: Typed this earlier when I had 5 mins to spare.

Another thing is to remind your GM that you have certain skills. No one can remember anything, so when your GM asks for a test of some sort, and you don't have the skill or it's linked to a really low stat, ask to change it out with another skill and stat that you are good that, which is relevant to the test at hand.

This is actually really important. Players not wanting to use their untrained skills and the GM forgetting what the players have at their disposal leads to a bit of an adversarial relationship between the two, but it's pretty natural.

Players really need to be like "Oh, oh, oh, I have Logic, can I logic this thing into submission?". GM:s can only moderate and suggest things so far, the players need to pull upon their own ingenuity when it comes to their characters.

Logic to help rewire plumbing? Sure, absolutely, go right ahead.

There's a lot of overlap in the skills of the WH40kRP, which isn't really a bad thing at all, but it requires some imaginative thinking, which should always be rewarded, as long as it's not utterly outlandish.

Using Logic as an Interaction Skill is also perfectly fine (maybe even using Fellowship, at some points), when you try to persuade someone with facts instead of lies, flattery or threats.

Logic as an Ad-Mech interaction skill is a great use of it. I also have it used in my games so that when players have some facts and clues but not enough direction with the plot of the game, that they can test it to piece the pieces together and get tips or ideas.
But yes, ultimately you should encourage each player to put forwards suggestions based on what skills they have. The GM should not be remembering every little thing each character has on their sheet.