Thompson:
Yes, a 'gill' is a quarter pint.
One fifth of a gill was the pre-metric standard measure (for a 'single' measure of spirits) in Scotland.
Down south the standard was slightly smaller at 1/6th of a gill. But at least this meant you could get an exact number of measures (32) from a standard spirits bottle.
A standard spirits bottle was 1/6th of a gallon (although usually stated in other measures - hence the connection in the quiz)

Cheers
Nigel