You are referring to the ticket named Swiss Travel Pass (SwissPass is another product).
The Swiss Travel Pass is a day pass. Its fixed validity starts at 0:00 midnight and ends at 5:00 a.m. the next day. You cannot adjust the times.
If you only arrive at 12 p.m., it makes little sense to use a day from the Swiss Travel Pass. Local tickets are the cheaper alternative. In Basel (and for completeness as well as in Lucerne), your hotel reservation works as a free ticket, to arrive from the BSL airport or Basel train station to the hotel using local public transport.
However, if you want to explore our country, Basel does not make the best base as it is located at proximity to the border and is therefore too far from the Alps.
Bern would make the better base.