There's two part of the question. First how voting works and 2 how to get the good timings.
First, voting for WL happens once the WC has reached Atomic Era. This happens either when someone reach information era or when half(rounded down) of the remaining civ have reached Atomic era. This means that you can either kill everyone but 2 and get to atomic or get to information.
Once you have reached the right era, the WL vote will happen after the first vote of that era. So the goal is to get a normal vote right after you reach the right era. This can be the first, the second or etc.
Now a couple of additional timings:
-Renaissance WC votes are 30 turns, Industrials 25 and Modern 20. This means that if the WC is still in Renaissance at the first vote then the next vote will also take 30 turns, but if someone reaches Modern (or half reach industrial) before the first vote then the next vote will happen in 25.
-When the WC changes era, it add 2 turns to whatever counter.
-When a vote occurs it also takes 1 turn
Now how to optimize it:
The WC is created when someone reaches PP and meet everybody so in essence everything is about when you make PP based on your expectation of when you will reach your goal era. You have two ways to do it. Either you create the WC very early and get an additional vote or you make it late.
For example if you make the WC on turn 130. Then you can expect 2 or 3 votes before getting your victory. Let's say the WC reaches industrial before the first vote too.
2 votes:
+30 first vote
+2 WC reaches Industrial (turn 162)
+1 Vote 1
+25 second vote
+2 WC reaches modern (before second vote)
+2 WC reaches atomic (before second vote)
This gives us 192. So if the WC reaches atomic before 192 (moment of the second vote which ) then 10(+1) turns later on turn 203 you will get the world leader vote.
Another example:
Let's say you delay the WC to turn 150.
+30first vote
+2reach indu
+2reach modern
+2reach atomic
This gives us a total of 186. So if WC reaches atomic before T186 you'll get your WL vote on turn 197.
Disclaimer: I may have made some mistakes by a couple of turns in these