When you travel with a Eurail pass in Italy needing or not needing reservations has little to do with how full or empty the train is but almost exclusively what grade of train you travel on.
Fast intercity trains are either Italo (the competition to the national railway company who have generally newer and often cheaper trains but who don't cover the whole country), Freccia trains (in 3 different colours indicated in their names, part of Trenitalia the national railway), or InterCities (the slowest of the Trenitalia faster trains, usually using quite old rolling stock).
You can't use Italo trains with the pass - they don't accept passes.
Passholders are required to purchase a reservation (included in the price of normal tickets but extra for passholders) for every leg of FReccia or IC trains. With the reservations you sit in car and seat on the reservation. All seats are reserved.
There are two other grades of trains in most of Italy. The Regionale and RV Regionale Veloce. These are like buses, there are no reservations needed or offered. You get on and find a seat somewhere, and if there are no seats you stand until one becomes available. Passholders don't need to buy reservations on R or RV trains, your pass is sufficient. These are the only trains in Italy where passholders retain freedom to hop on and hop off.