changing trains at pisa at 3:30 a.m in the night

I would not worry about safety; I would worry that if you are changing in Pisa at 3:30, you will be in Florence at 5:00, and probably half awake and half asleep as your night rest - if any - has been interrupted in the middle of the night. What are you going to do in Florence at 5am?

I agree, the real issue is what will you do when you arrive? If you are checking into a hotel, you may be able to get a room that early, but an apartment or B&B will probably not be available at that hour.

Why would you do this? It's not a safety issue but a sanity issue.

Right. Besides arriving with little-to-no sleep and attractions/accommodations not being open/available for hours, the trains running that time of day are intercity/regionales that take 8 hours or more and make lots of stops!

I'm curious why this versus take an earlier/later train that can get you there in as little as 3:16 hours and allow you to get some sleep?

There are 15 trains a day that can get you from Salerno to Florence in 3 to 4 hours, many with no change and you are choosing the only one option that takes you 9 hours.
Don't know what to say.

Bought into the idea that a night train saves money because you don't have to get a hotel room. That was slightly valid when there were true night trains with beds.

When trains were relatively slow and air fares expensive, only trains going from the very South of Italy (Sicily or Calabria or Puglia) to the very north made sense; the shorter Rome to Milan night train had to run very slowly along a circuitous itinerary in order not to arrive too early.

But now there are fast trains and low cost airlines. If you need to be somewhere early usually the very first fast train in the morning will deliver you to destination early enough if your travel is within the 600 kms range. For longer itineraries, flying is now more convenient and no more expensive than train. So most night trains in Italy (and all over Europe) are being phased out as they do not have a market anymore. The few remaining night trains are on the very long itineraries (I guess for those who are afraid of flying) and using their intermediate stops in the middle of the night, while possible, makes little sense.

I love traveling by Italian rail. I do. But 8-9 hours overnight by regionale/intercity when you can do it so much faster is daft.

Thank you everyone for your valuable suggestions. I have decided to stay overnight at Salerno and leave for Florence early next morning.

Rhlkochar, good for you for changing your plans. And good for you for coming here to ask about them. You are going to be very glad you're doing it this way.