The museum gave it away, they have an excellent website to look at their collection.
My first thought was the SIAD (Società Italiana Automobili Darracq, A 1908 Darracq 8/10 HP assembled by Alfa Romeo's predecessor, Darracq Italiana) at the Museo Storico Alfa Romeo, but it was not, hence to start looking for a similar 1906 car.
LEGNANO mod. A 6/8 HP
This little two-seater with its “duc” coachwork and snub-nosed radiator was made by FIAL (Fabbrica Italiana Automobili Legnano), a small company that operated in Lombardy from 1906 to 1909. It has a front-mounted, integral two-cylinder engine, a sheet steel chassis and cardan shaft drive, and cost 4000 lire.
Engine: 2 cilindri
Capacity: 1135 cc
Max power output: 8 CV a 1100 giri/min.
Max speed: 55 km/h
Weight: 420 kg