When I was in college, I took a writing class that used some version of Technical Communication by Mike Markel. It seems to be targeted mostly at native speakers (which most or all of my class was) but there is a small section aimed at non-native speakers which has a mixture of helpful cultural advice for interacting with Americans, and English language advice that seems too basic to help anyone who is proficient enough to read an English language textbook. Still, the rest of the book is solid.
Some of the advice given is for other types of technical communication (e.g. making graphics) but a lot of it is writing advice. For example, about parallel constructions:
When using parallel constructions, make sure that parallel items in a series do not overlap, causing confusion or even changing the meaning of the sentence:
confusing: The speakers will include partners of law firms, businesspeople, and civic leaders.
Partners of appears to apply to businesspeople and civic leaders, as well as to law firms. That is, partners of carries over to the other items in the series.
The following revision solves the problem by rearranging the items so that partners can apply only to law firms.
clear: The speakers will include businesspeople, civic leaders, and partners of law firms.
Of course, you would still need to apply this to your writing, which is far more difficult. As always, it would be helpful to read good writing, practice, and get feedback from someone who knows what they're doing (even a grammar checker can be helpful if you use it to detect improvements without blindly trusting it).
