the mayor is on the council
Commonly, in the UK a councellor is said to be ON the council, ie a member of it. In the council would mean physically present in the venue.
Each is acceptable here, in my opinion.
A quick search for "ar an gcomhairle" turns up quite a few hits, which suggests that "sa chomairle" and "ar an gcomhairle" may have the same two different meanings in Irish that they do in English - in the council and on the council.
In Ireland it is always said "on the council"
Why then is it not accepted in the previous sentence to write "the new senators are in the Senate"? Both constructions are stictly parallel.
The exercises are delivered randomly. Your "previous sentence" won't always be the same as someone else's previous sentence.
Assuming you are talking about Tá seanadóirí nua sa Seanad, they aren't strictly parallel, because there is no definite article in Tá seanadóirí nua.
You have found an oddity of English - you may as well ask why it is "in the morning" but "at night".