Please forgive if this doesn't help to answer your question. Take a look at these screen shots. I'm using SH3 Commander and GWX 3.0. I have days in base set to "random" in SH3C
First.. Game load screen. As you describe, patrol end and patrol start on the same day. January 1, 1942
In the office before mission, still says January 1st.
Then, once on patrol.. Note the date February 24, 1942.