Theorem 1.2.3 (p18) of 

MOHAMED HACHMI SLIMAN
Théorie de Mackey pour les groupes adéliques
Astérisque, tome 115 (1984) [Link at SMF site](https://smf.emath.fr/download/pdf/107560)

asserts that the $F$-points of linear algebraic groups over characteristic zero local fields $F$ are of type 1.  The author states the result in a slightly more general setting that allows for some covering groups.