Looking at the player aid included in the game, under "County Assessment", the first term is Mayor.
As written, the core game has you adding score to the player with the Mayor role whenever a white cube is built over. So I am not understanding why Mayor is listed for that phase. The mayor is not referenced in the rules under the County Assessment rules.
If you use the "Power of Elections" variant, found in the companion guide, the Mayor points will not be awarded until the election is resolved. So again, I don't understand why the Mayor is referenced on the player aid.
And a final unimportant question... what is the train piece for? I assume it is for tracking your VP. But the rules don't mention it.
I actually noticed that this past weekend. I had an opportunity to play Forged in Steel for the first time since the game arrived. As I was explaining the first scoring phase it occurred to me that was not a part of Scoring. I usually teach without referring to rules/player aids and I never caught it before we sent the final files.
To be honest, I am not sure what I was thinking when that was added to the player aid? Those player aids were created over two years ago. My guess is that it is a holdover from an older player aid that used an entirely different mechanism for scoring the Mayor role. Originally, the player that won the Election scored a flat 8 VP. It was not until we began the final development did we factor in that the City Ownership cubes generated the Mayor scoring. The only catch is that should have still been something that was determined in The Elections phase.
The train tokens was a KS stretch goal. You are right, though. They are used to mark the Scoring Track.