Dynamically display link only when viewing the last post in a category

Hey folks, here’s what I want to have happen:

I have multiple categories for posts. I already have WP set up to only move readers along posts within the same category. When a user is reading the last/most recent post in the first category, I want to generate a link to push them to category 2, so as to not roadblock them and help guide the user flow.

I am stuck on how I can determine in the single-post.php template whether or not a post is the last/most recent in a category, and therefor display the desired link.

Hopefully my description makes sense… Any help is greatly appreciated