Unlike the first season this one became more episodic in my opinion. The sole reason I watched this really is because Yuuichi Nakamura voiced the main character, Takasugi Shinsaku. It also has a couple more popular voice actors in it. Anyway, so the plot is that the chronometer returns and goes berserk from being cut by Takasugi in the first season. As if that wasn't enough, a new Mugensai shows up. So the chronometer does some weird stuff and the characters go and solve the problem, until about 7 or 8 episodes in, does it follow more of a story. Honestly some parts of the story made me raise an eyebrow thinking "Really?"
Anywho, the thing I was honestly more excited about was the ending omake's. I would have honestly watched something like an iyashikei with this cast more than the clustertruck that was the first season and the last couple episodes of this show.
Now what I REALLY appreciate is them leaving out the "woman". Being intrigued by the charcters after watching the show, I downloaded the app to see what it was like and yeah, it's one of those dating sims. My Japanese just wasn't on the level to really play the game because I was interested to see in what regards the game ties in with the anime (what I got was really the characters; and Seimei giving you the chronometer, which throws you back in time to the Bakumatsu era). I quickly dropped the game though as I saw it had the five tickets a day system. The game descriptions is also what threw off a lot of people I think. I remember from the first season where a lot of people were asking "Where's the woman?"
I found that the animation and artstyle was consistent a lot, except towards the last couple episodes where it fell a little. But still it never got unwatchably bad. I liked the opening animation and song a lot as well. The ending omake's I mentioned were more chibified but still really fun to watch.
Anyway, if you're just looking for something to watch, I'd honestly give this a show. It is obviously geared more towards women with the ikemen and Takasugi's boob window (seriously I think that tube top is just body paint). The first season can be a little overwhelming(?) since it is very high paced and a lot of characters are thrown at you at once. I found them a little easier to remember since I've seen virtually all Gintama episodes and knew the names from the Shinsengumi etc.