Was Hesse-Kassel neutral? And Westphalia's territory was not just from Hesse-Kassel, but also from Brunswick, parts of Hanover and Prussia's western provinces.
Hesse-Kassel was on the side of the allies at least from 1793-1795 as they received British subsidies in order to fight the French. They also received subsidies from 1801-1802 and 1804 and 1806 from claims for past service against the French. They also received British subsidies in 1807.