John Locke was a philosopher who's commonly known as the father of liberalism. Another important figure from that period was Jean-Jacques Rousseau.
Of course, there are many others to consider...List of political philosophers
Are there major gaps I need to fill to even make sure I have a grasp
of these, or can I move on?
You said you took this course over a year ago. So it sounds like you have a genuine interest in political philosophy and want to expand on what you learned in your course.
If you want to learn what others have written about political philosophy, then you're on the right track. But if you really want to understand "politics," there's no substitute for experience (combined with studies).
I've been involved in political activism for some time, and my experiences definitely influence my thoughts about philosophy, which I began studying just a year or two ago. I occasionally read things written by famous philosophers that really resonate with me. (I just recently discovered that Machiavelli wrote a "book" about conspiracy!) But, of course, there are other things I don't agree with. And there are many philosophical ideas that simply don't make sense to me.
Part of the problem is the fact that the world has changed so much. If Locke, Rousseau and Karl Marx were alive today, they'd probably do a backwards somersault over global population growth, the scale of modern warfare, the Internet and social media, and on and on.
In fact, there are few major philosophical figures who had much to say about the environment (to my knowledge). Reading a novel by Edward Abbey or Aldo Leopold (Desert Solitaire and Sand County Almanac were my bibles when I was in college) will probably give you more enviro-philosophical insights than the combined writings of every major philosopher from Plato up to the early 20th century.
It's really striking that the last giants among political philosophers lived over a century ago. Some would disagree, but it's certainly hard to name any contemporary political philosophers who really have any stature. In addition, philosophy has been increasingly tainted by propaganda.
Perhaps I should make an exception for Jean-Paul Sartre (1905-1980), a popular French philosopher associated with existentialism. He was a huge fan of Che Guevara, which makes him a bit of a maverick. Albert Camus (1913-1960) was another French philosopher commonly associated with existentialism, though he preferred to call himself a student of absurdism.
So what should we do in the face of a universe that makes no sense, commit suicide? "No!" said Camus - "We should revolt." (I'm paraphrasing.)
But how can you understand mammals if you live on a tropical island inhabited only by birds? A combination of life/political experience and philosophical studies have given me insights into the ideas of famous politicos, good and evil, from Che Guevara to Obama, Adolf Hitler to Genghis Khan.
In summary, if you really want to understand political philosophy, you need to get out in the real world and observe what's going on. Don't just study philosophers' writings; walk in their shoes. Discuss politics with a variety of people - working class stiffs who are working two or three jobs to pay the rent, yuppies and homeless people. If you really want your eyes opened, run for public office. Even a lowly school board campaign in a major city can be a mind-boggling experience.
To be brutally blunt, most of the people who discuss political philosophy on forums appear to me to be armchair philosophers with very little life experience. It really shows in their comments.