We've booked opening day on Southwest quite a bit. I'm not sure what time of day they open, but we've never seen much fluctuation on prices during the first couple of days unless it's a high-demand route, like to Nashville to Orlando during fall break. High demand routes you will want to book ASAP. Their fares will fluctuate some -- usually going up as the plane fills, but they will drop quite often too. Only in one case did I see the price drop enough to make it worth rebooking for me. That was something like a $75 per ticket drop -- when you have four tickets, that adds up. If it's just $5-$10 dollars a ticket, I may not bother. Depends on if we are flying again soon.
About rebooking -- if you aren't familiar with Southwest, if the price drops, you can change your reservation with no fees and rebook the exact same flight and get refunded the difference. The type of refund will vary, based on if you used points, a full price fare, or a Wanna Get Away fare. If you book with points, the difference in points is fully refunded to your account. Full fare tickets get a full refund of the price difference. Wanna Get Away refunds are done as credits -- you would get a credit that can be used toward another ticket, but that credit has to be used for travel within one year of the date of purchase of the original ticket. For example, if you bought a ticket on June 22, 2017, then got a refund credit, you would to take (not just book - but take) another flight before June 22, 2018 to use the credit.