Hi!
I know this is super late and you probably already have the answer but I am a student and was searching for the answer to this question today. I figured if I posted my answer, other students could look here and stop. Anyway, type 1 immune response can also be thought of as "Cell-mediated or type 1 immunity" which "includes production of gamma interferon (IFN-γ) and generation of cytotoxic CD8 T cells."
This Baldwin paper evaluates Type 1 immune response and defines what they mean by "Type 1 immune response". Type 1 Hypersensitivity would be a different response (I believe). Thanks!
Evaluation of Type 1 Immune Response in Naïve and Vaccinated Animals following Challenge with Leptospira borgpetersenii Serovar Hardjo: Involvement of WC1+ γδ and CD4 T Cells
https://iai.asm.org/content/70/11/6147.full