A period during which Jews fasted over the temple and the death of governor Gedaliah, referred to at Zechariah 1:12 and Zechariah 7:5. This period ran from 587 BCE (temple destroyed (fifth month) and Gedaliah killed (seventh month)) until 517 BCE (Darius' fourth year).
We agree that the JWs are incorrect in referring to the 70 years of Zechariah as the same 70 years of Babylonian domination mentioned at Jer. 25:11 (or as they see it, 70 years of Jewish exile in Babylon) , but some argue that Zech. is referring to two 70-year periods, not just the one you mentioned. And each of those two periods are (were) ongoing and do not refer back 20 years to the end, or fullfilment, of the 70 years of Jeremiah 25:11.
As you correctly point out, in Zech. 7:5," this period ran from 587 BCE (temple destroyed (fifth month) and Gedaliah killed (seventh month)) until 517 BCE (Darius' fourth year)". But if 1:12 and 7:5 refer to the same 70 years, isn't there a two-year discrepancy between the 2nd year of Darius of 1:12 (519/20) and the 4th year of Darius at 7:5 (517/18)? The context of 1:12 seems to indicate that the continued desolate condition of the temple, as it was still in ruins, was the object of the plea for YHWH to have mercy (i.e., please Lord, have mercy and help us restore the temple). And in 1:16 (the context of the plea) YHWH would turn to Jerusalem and show Israel mercy and build his house, the temple. How are the 2 years between Darius' second and fourth year reconciled in order to make them the same 70-year-period? Some might argue that 1:12 was just a vision looking forward, or something murky like that. The Zech. 1:12 70 years amount to only 68 years if one counts back to 587.
Some, like the Catholics, get around the 70 years by claiming they all are mere periods of time, one vague generation, and not to be taken literaly. Not sure if I go along with that, but it's plausible.