Take a look at this:
It is specific to T1 and it considers the merits of stuff that has a clear role with T2. The relevant sub-section is the stuff on GLP-1. My understanding of GIP, which is slightly different, comes from this article:
https://www.sciencedirect.com/science/article/abs/pii/S1521690X09000207
That suggests you need beta cells. There is stuff in the first paper about LADA and MODY. My very, very, limited understanding is that you probably want to get a C-peptide test before you start to make sure you still have some insulin production (see the C-peptide test stuff and “Figure 1” about diagnosis) and make absolutely sure you have an up-to-date diagnosis.
Here’s the main thread on the first paper: