Here is the schedule for November which will not be much different in Feb
There are trains every 1/2 hour all day long. Leave Florence Santa Maria Novella station at 8:28,9:28,10:28 on an RV train which takes 1 hour. Return at 13:32,14:32,15:32,16:32,17:32 also on a train which takes an hour.
There are trains in between these times which take 1 hour 17 minutes.
Book 2nd class. You can buy the tickets at the station from a ticket machine which will "speak" to you in English. No need to purchase early as tickets cost Euro 7.80 & are not discounted. I found what happened to you, i.e., Feb shows tickets via Roma on the Red Arrow trains. Nevermind! The trenitalia system here does not show the regional train schedules until the week before the service. ....don't even ask why.....
You will be fine. I suggest that you plan to walk through the old part of Pisa next to the Piazza dei Miracoli after you have seen the tower, etc. You might also want to stroll along the Arno. Happy trails!