Translation:During the campaign every candidate says that he wants to reduce taxes.
As a Finn I am used to speak and write in a gender neutral way (since the Finnish language doesn't have a separate word for 'she' and 'he'), and for me all these masculine pronouns being used as the norm seem weird. Could this be translated as "every candidate says they want to..." or does this refer to a male candidate only?
"He" used to be neutral and/or default. This is very common in many languages. But people began to associate identity for some odd reason with grammar, as if the latter dictated the former, and now something that was neutral has become a very emotionally charged issue. I do think "they" is a good way out of it and how most people talk if you listen, but it's important to remember that "he" is a grammatical denomination, and grammar doesn't care about your definition of self and it certainly has never been successfully changed bt force
Google gives 277.000 hits for "in campaign time", and they are related to politics. We are dealing with a political "campaign" here. "During the campaign" contains many references to military campaigns. Just Google it. The first hits for "during the campaign" that I get refer to Duryee's Brigade (never heard of), Von Moltke, etcetera.
You probably forgot to put it in quotation marks. There are significantly less hits than you suggested. If you scroll through the results you even get as few as 116.
Anyways, Google is not the most reliable source, as many texts on the internet may have been written by non-native speakers.
Btw, check out the Corpus and see for yourself that 'during the campaign' isn't in fact used in the context of war in the vast majority of cases.
I did not google "in campaign timeS" (plural) but "in campaign time" (singular). "In campaign times" is indeed unidiomatic, it's not even English. Almost all hits for that phrase contain a comma break: "in campaign, times..." with times being the start of a new subsentence.