LinkedIn is a good idea - it is strange how it is so underused in the education sector.
About ten years ago I went on a LinkedIn ‘sprint’ and got myself from about 200 to 500+ connections in a matter of weeks.
I am writing this in case it helps anyone else to get started.
Apart from the obvious starting points of colleagues, ex-colleagues and friends, I added:
People with whom I had worked with on projects, however briefly
Fellow students on courses
CPD trainers
Key figures in my field, who often want to connect with anyone as they are that kind of person.
LinkedIn limits the number of searches that you can do per month, so sometimes it can be helpful to search on Google first to find someone.
I never worry about writing the ‘personal note’ with an invitation as I figure that someone will either want to connect or they won’t.
I now have 600+ connections and review them annually, removing some each time if they are inactive and/or not really doing anything beyond a straightforward role. But for me it’s not about job status - they might be a low-paid worker in my sector but if they are involved in projects, studying or doing something that connects with others, then I am keen to stay connected.
Finally, you don’t need to fill in every section on your profile, especially if you’re in a state of transition or not working. I am currently self employed so deleted all my jobs a while back and just have a detailed longhand description of myself in my profile. No one seems to mind!