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.